FILING PURSUANT TO RULE 424(b)(2)
                                           REGISTRATION STATEMENT NO. 333-115195

                           PROSPECTUS SUPPLEMENT NO. 4
                        (TO PROSPECTUS DATED MAY 5, 2004)

                                GERON CORPORATION

                      WARRANTS TO PURCHASE COMMON STOCK AND
                 COMMON STOCK ISSUABLE UPON EXERCISE OF WARRANTS

         You should read this prospectus supplement and the accompanying
prospectus carefully before you invest. Both documents contain information you
should consider carefully before making your investment decision.

         We are amending warrants to purchase 2,295,082 shares of common stock,
which are exercisable from time to time beginning December 20, 2007 until
November 10, 2011 (the "Warrants"). The exercise price shall be $7.50 per share
during the period from December 20, 2007 until December 15, 2009. If, on
December 15, 2009, the average of the closing bid prices of the Common Stock for
the five trading day period ending on December 15, 2009 is below $7.50, then the
exercise price shall equal to such lower price, but shall be no less than $6.80
per share. We will receive immediate proceeds from the sale of these Warrants
equal to approximately $1,678,779. We will receive maximum proceeds of
approximately $17.2 million upon the full exercise of the Warrants (less our
expenses relating to such exercise, which are estimated to be $15,000).

         In the event that we are acquired for consideration, consisting wholly
or in part of cash, by a company whose stock does not trade on one of certain
leading exchanges, the holders of these amended and restated warrants may
exchange their warrants for the theoretical value of those warrants, based on a
Black-Scholes valuation.

                LIMITATION ON THE USE OF OUR NET OPERATING LOSSES

We have significant amounts of net operating loss ("NOL") carry forwards (as of
December 31, 2006, domestic federal NOL carry forwards of approximately
$319,700,000, which will expire at various dates beginning 2007 through 2026, if
not utilized). These NOLs may be used to offset future taxable income, to the
extent we generate any taxable income, and thereby reduce or eliminate our
future federal income taxes otherwise payable. However, the Internal Revenue
Code of 1986, as amended, imposes significant limitations on the utilization of
NOLs in the event of an "ownership change," as defined in Section 382 of the
Code. This Section 382 limitation is an annual limitation on the amount of
pre-ownership change NOLs that a corporation may use to offset its
post-ownership change income. We may or may not have experienced an ownership
change as a result of events in the past and/or the sale of shares of common
stock and Warrants pursuant to this prospectus supplement (or a combination
thereof). If so, the use of our NOLs (or a portion thereof) against our future
taxable income may be subject to a limitation under Section 382.

                    MATERIAL U.S. FEDERAL TAX CONSIDERATIONS

         The following is a general discussion of the material U.S. federal
income tax consequences of the ownership and disposition of our common stock and
Warrants by holders holding the common stock or Warrants, as the case may be, as
capital assets (generally, property held for investment), but is not a complete
analysis of all the potential tax consequences relating thereto. This discussion
is limited to holders who purchased the common stock and Warrants they hold as
part of investment units (each, a "Unit") pursuant to prospectus supplement No.
1 to the prospectus dated May 4, 2004 contained in our registration statement
no. 333-115195. In addition, this discussion assumes that neither the amendments
to the terms of the Warrants nor any payments made by the holders with respect
thereto will, separately or in the aggregate, cause a deemed exchange of the
Warrants or, in the event that there is such a deemed exchange, that such deemed
exchange would be a tax-free recapitalization for U.S. federal income tax
purposes. For the purposes of this discussion, a U.S. Holder is any beneficial
owner of our common stock or Warrants that is treated for U.S. federal income
tax purposes as:



     o    an individual citizen or resident of the United States;

     o    a corporation  (or other entity taxable as a  corporation)  created or
          organized in the United  States or under the laws of the United States
          or any political subdivision thereof;

     o    an  estate  whose  income  is  subject  to  U.S.  federal  income  tax
          regardless of its source; or

     o    a trust (x) if a court  within the United  States is able to  exercise
          primary  supervision over the  administration  of the trust and one or
          more  United  States   persons  have  the  authority  to  control  all
          substantial  decisions  of the  trust  or (y)  which  has made a valid
          election to be treated as a United States person.

         If a partnership holds our common stock or Warrants, the tax treatment
of a partner will generally depend on the status of the partner and upon the
activities of the partnership. Accordingly, partnerships which hold our common
stock and partners in such partnerships should consult their own tax advisors.

         This discussion does not address all aspects of U.S. federal income
taxation that may be relevant in light of a holder's special tax status or
special circumstances. U.S. expatriates, insurance companies, tax-exempt
organizations, dealers in securities, banks or other financial institutions,
"controlled foreign corporations," "passive foreign investment companies,"
"foreign personal holding companies," corporations that accumulate earnings to
avoid U.S. federal income tax, U.S. expatriates, U.S. Holders whose functional
currency is not the U.S. dollar, tax-exempt organizations, and investors that
hold our common stock as part of a hedge, straddle or conversion transaction are
among those categories of potential investors that are subject to special rules
not covered in this discussion. This discussion does not address any tax
consequences arising under the laws of any state, local or non-U.S. taxing
jurisdiction. Furthermore, the following discussion is based on current
provisions of the Internal Revenue Code of 1986, as amended, and Treasury
Regulations and administrative and judicial interpretations thereof, all as in
effect on the date hereof, and all of which are subject to change, possibly with
retroactive effect. Accordingly, each Non-U.S. Holder should consult its own tax
advisors regarding the U.S. federal, state, local and non-U.S. income and other
tax consequences of acquiring, holding and disposing of shares of our common
stock.

U.S. HOLDERS

Dividends Paid on Common Stock

         A U.S. Holder generally will be required to include in gross income as
ordinary dividend income the amount of any distributions paid on the common
stock to the extent that such distributions are paid out of our current or
accumulated earnings and profits as determined for U.S. federal income tax
purposes. Distributions in excess of such earnings and profits will reduce the
U.S. Holder's tax basis in its common stock and, to the extent such excess
distributions exceed such tax basis, will be treated as gain from a sale or
exchange of such common stock. Corporate holders may be entitled to a dividends
received deduction with respect to such distributions and are urged to consult
their own tax advisors in this regard. With respect to non-corporate U.S.
Holders for taxable years beginning before January 1, 2011, dividends may be
taxed at the lower applicable capital gains rate provided that certain holding
period requirements are met.

Disposition of Common Stock

         Upon the sale or other disposition of common stock, a U.S. Holder
generally will recognize capital gain or loss equal to the difference between



the amount realized on the sale and such holder's adjusted tax basis in the
common stock. A U.S. Holder's tax basis in its common stock will equal that
portion of the cost of the Unit that is allocated to the common stock (based on
the relative fair market values of the common stock and the Warrant comprising
the Unit at the time of issuance). Gain or loss upon the disposition of the
common stock will be a long-term if, at the time of the disposition, the holding
period for the common stock exceeds one year.

Tax Treatment of Warrants

         A U.S. Holder will recognize gain or loss upon the sale, redemption,
lapse or other taxable disposition of a Warrant in an amount equal to the
difference between the amount of cash and the fair market value of other
property received (if any) by the U.S. Holder and the U.S. Holder's tax basis in
the Warrant. A U.S. Holder's tax basis in a Warrant should equal that portion of
the cost of the Unit that is allocated to the Warrant (based on the relative
fair market values of the common stock and the Warrant comprising the Unit at
the time of issuance) plus the allocable portion of the amount paid by the
holder with respect to the Warrants. Such gain or loss will be capital gain or
loss if the common stock to which the Warrants relate would be a capital asset
in the hands of the Warrant holder and will be long-term capital gain or loss if
the holding period exceeds one year.

         The cash exercise of a Warrant will not, and the cashless exercise of a
Warrant should not, be a taxable event for the exercising U.S. Holder, except
with respect to cash, if any, received in lieu of a fractional share. The
Internal Revenue Service (the "IRS") may argue, however, that the surrender of
one or more Warrants in payment of the exercise price of another Warrant upon a
cashless exercise results in taxable gain or loss to the exercising U.S. Holder
in an amount equal to the difference between the exercise price deemed paid and
the tax basis in the Warrant surrendered for payment of the exercise price. A
U.S. Holder will generally have a holding period in shares of common stock
acquired upon exercise of a Warrant that commences on the day after the date of
exercise of the Warrant. With respect to the cashless exercise of a Warrant, it
is possible that a U.S. Holder may have a holding period in shares of common
stock received in exchange for the surrender of one or more Warrants which
includes the holding period of the Warrants so surrendered.

         If the exercise price is nominal, it is possible that the Warrants may
be deemed to have been exercised for tax purposes on the date on which they
first became exercisable or possibly on the date issued, regardless of whether
they are actually exercised on the date on which they are first exercisable. As
a result, it is possible that the holding period of shares of common stock may
be deemed to have begun on the date on which the Warrants first became
exercisable or possibly on the date issued.

         An adjustment to the exercise price or conversion ratio of the
Warrants, or the failure to make such adjustments, may in certain circumstances
result in constructive distributions to the holders of the Warrants that could
be taxable as dividends under Section 305 of the Code. In such event, a holder's
tax basis in the Warrant would be increased by the amount of any such dividend.

NON-U.S. HOLDERS

Dividends Paid on Common Stock

         Payments on our common stock will constitute dividends for U.S. federal
income tax purposes to the extent paid from our current or accumulated earnings
and profits, as determined under U.S. federal income tax principles. Amounts not
treated as dividends for U.S. federal income tax purposes will constitute a
return of capital and will first be applied against and reduce a holder's
adjusted basis in the common stock, but not below zero, and then the excess, if
any, will be treated as gain from the sale of the common stock (the tax
treatment of which is described below).



         Amounts treated as dividends paid to a Non-U.S. Holder of common stock
generally will be subject to U.S. withholding tax either at a rate of 30% of the
gross amount of the dividends or such lower rate as may be specified by an
applicable tax treaty. In order to receive a reduced treaty rate, a Non-U.S.
Holder must provide a valid IRS Form W-8BEN or other successor form certifying
qualification for the reduced rate.

         Dividends received by a Non-U.S. Holder that are effectively connected
with a United States trade or business conducted by the Non-U.S. Holder are
exempt from such withholding tax. In order to obtain this exemption, a Non-U.S.
Holder must provide a valid IRS Form W-8ECI or other successor form properly
certifying such exemption. Such effectively connected dividends, although not
subject to withholding tax, are generally taxed at the same graduated rates
applicable to United States persons, net of allowable deductions and credits.

         In addition to the graduated tax described above, dividends received by
a corporate Non-U.S. Holder that are effectively connected with a United States
trade or business of such holder may also be subject to a branch profits tax at
a rate of 30% or such lower rate as may be specified by an applicable tax
treaty.

         A Non-U.S. Holder may obtain a refund of any excess amounts currently
withheld if an appropriate claim for refund is filed timely with the IRS. If a
Non-U.S. Holder holds our common stock through a foreign partnership or a
foreign intermediary, the foreign partnership or foreign intermediary will also
be required to comply with additional certification requirements.

Tax Treatment of Warrants

         An adjustment to the exercise price or conversion ratio of the
warrants, or the failure to make such adjustments, may in certain circumstances
result in constructive distributions to the holders of the warrants that could
be taxable as dividends under Section 305 of the Code and subject to the
withholding described above. In such event, we intend to withhold any applicable
withholding tax from any subsequent distributions of cash or property made to a
Non-U.S. holder, including any common stock issued by us upon the exercise of a
warrant.

Gain on Disposition of Common Stock or Warrants

         A Non-U.S. Holder generally will not be subject to U.S. federal income
tax on any gain realized upon the sale or other disposition of our common stock
or Warrants unless:

     o    the  gain is  effectively  connected  with a  United  States  trade or
          business  of the  Non-U.S.  Holder  or, if a tax  treaty  applies,  is
          attributable to a United States permanent establishment  maintained by
          such Non-U.S. holder;

     o    the  Non-U.S.  Holder is an  individual  who is  present in the United
          States for a period or periods aggregating 183 days or more during the
          taxable  year in  which  the  sale or  disposition  occurs  and  other
          conditions are met; or

     o    our common stock or Warrants  constitute a United States real property
          interest  by reason of our status as a "United  States  real  property
          holding corporation" (a "USRPHC") for U.S. federal income tax purposes
          at any time within the shorter of the five-year  period  preceding the
          disposition or the holder's holding period for our common stock.

         We believe that we are not currently and do not expect to become a
USRPHC. However, because the determination of whether we are a USRPHC depends on
the fair market value of our United States real property interests relative to
the fair market value of our other business assets, there can be no assurance
that we will not become a USRPHC in the future.



         Unless an applicable treaty provides otherwise, gain described in the
first bullet point above will be subject to U.S. federal income tax imposed on
net income on the same basis that applies to United States persons generally
and, for corporate holders under certain circumstances, the branch profits tax,
but will generally not be subject to withholding. An individual Non-U.S. Holder
described in the second bullet point above will be subject to a flat 30% tax on
the gain derived from the sale, which may be offset by United States source
capital losses. Non-U.S. Holders should consult any applicable income tax
treaties that may provide for different rules.



         Our common stock is quoted on the Nasdaq Global Market under the symbol
"GERN." On December 19, 2007, the last reported sale price of our common stock
on the Nasdaq Global Market was $6.08 per share. As of December 19, 2007, we had
76,015,669 shares of common stock outstanding.

         Investing in our common stock involves certain risks. See "Risk
Factors" beginning on page 1 of the prospectus, including the specific risks set
forth under the caption "Additional Factors That May Affect Future Results" and
incorporated by reference from the Company's filings made with the Securities
and Exchange Commission under the Securities Exchange of Act, as amended,
between the date of the prospectus and the termination of the offering.

         You should rely on the information provided or incorporated by
reference in this prospectus supplement and the prospectus. We have not
authorized anyone else to provide you with different information. You should not
assume that the information in this prospectus supplement is accurate as of any
date other than the date on the front of these documents.

         Neither the U.S. Securities and Exchange Commission nor any state
securities commission has approved or disapproved of the securities or passed
upon the accuracy or adequacy of this prospectus. Any representation to the
contrary is a criminal offense.

         The date of this prospectus supplement is December 21, 2007.



                                                                                             
                               TABLE OF CONTENTS

                                   PROSPECTUS

About this Prospectus                                                                             1
About Geron                                                                                       1
Risk Factors                                                                                      1
Forward-Looking Statements                                                                        2
Ratio of Earnings to Fixed Charges                                                                2
Use of Proceeds                                                                                   2
Plan of Distribution                                                                              2
Description of Debt Securities                                                                    4
Description of Common Stock                                                                      12
Description of Preferred Stock                                                                   13
Description of Warrants                                                                          15
Certain Provisions of Delaware Law and of the Company's Charter and Bylaws                       16
Legal Matters                                                                                    17
Experts                                                                                          17
Limitation on Liability and Disclosure of Commission Position on
Indemnification for Securities Act Liabilities                                                   17
Where You Can Find More Information                                                              18