WASHINGTON, D.C. 20549


                                    FORM 8-K

                                 CURRENT REPORT
                     PURSUANT TO SECTION 13 OR 15(D) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

      Date of Report (Date of Earliest Event Reported): September 19, 2005

                                GERON CORPORATION
             (Exact name of registrant as specified in its charter)

          Delaware                      0-20859               75-2287752
(State or other jurisdiction   (Commission File Number)     (IRS Employer
      of incorporation)                                   Identification No.)

                             230 CONSTITUTION DRIVE
                          MENLO PARK, CALIFORNIA 94025
          (Address of principal executive offices, including zip code)

                                 (650) 473-7700
              (Registrant's telephone number, including area code)

          (Former name or former address, if changed since last report)

Check the appropriate box below if the Form 8-K filing is intended to
simultaneously satisfy the filing obligation of the registrant under any of the
following provisions (see General Instruction A.2. below):

|_|  Written communications pursuant to Rule 425 under the Securities Act (17
     CFR 230.425)

|_|  Soliciting material pursuant to Rule 14a-12 under the Exchange Act (17 CFR

|_|  Pre-commencement communications pursuant to Rule 14d-2(b) under the
     Exchange Act (17 CFR 240.14d-2(b))

|_|  Pre-commencement communications pursuant to Rule 13e-4(c) under the
     Exchange Act (17 CFR 240.13e-4(c))

Item 8.01      Other Events.

     The Company deems the following information to be material:

     On September 20, 2005, Geron Corporation (the "Company") announced that, on
Monday, September 19, 2005, the underwriters of its public offering of six
million shares of common stock exercised their over-allotment option in full to
purchase 900,000 additional shares.

     The Company's press release dated September 20, 2005, announcing the
over-allotment exercise is attached here as Exhibit 99.1 to this Current Report
on Form 8-K and is incorporated herein by reference.

     Forward-Looking Statements. This report may include forward-looking
statements within the meaning of Section 27A of the Securities Act of 1933, as
amended, and Section 21E of the Securities Exchange Act of 1934, as amended (the
"Securities Exchange Act"). These statements relate to future events, including
future capital raising events. In some cases, you can identify forward-looking
statements by terminology such as "may," "will," "should," "expects," "plans,"
"anticipates," "believes," "estimates," "predicts," "potential" or "continue" or
the negative of those terms and other comparable terminology. These statements
reflect only management's current expectations. Important factors that could
cause actual results to differ materially from the forward-looking statements we
make or incorporate by reference in this report are set forth under the heading
"Risk Factors" in our Prospectus Supplement filed under Rule 424(b) under the
Securities Act of 1933, as amended, on September 16, 2005, and our most recent
Annual Report on Form 10-K, Quarterly Reports on Form 10-Q and Current Reports
on Form 8-K, as may be updated from time to time by our future filings under the
Securities Exchange Act. If one or more of these risks or uncertainties
materialize, or if any underlying assumptions prove incorrect, our actual
results, performance or achievements may vary materially from any future
results, performance or achievements expressed or implied by these
forward-looking statements. We disclaim any intent or obligation to update these
forward-looking statements.

Item 9.01.     Financial Statements and Exhibits

               (a)  Financial Statements.


               (b)  Pro Forma Financial Information


               (c)  Exhibits:

                        99.1     Press Release of Geron Corporation, dated 
                                 September 20, 2005.


     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.

                                             GERON CORPORATION

Date: September 20, 2005                     By: /s/ David L. Greenwood
                                                     David L. Greenwood
                                                     Executive Vice President
                                                     Chief Financial Officer