<PAGE>   1
   AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON SEPTEMBER 20, 1996
                                                    REGISTRATION NO. 333-05853

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                         POST-EFFECTIVE AMENDMENT NO. 1
                                       TO
                                    FORM S-1
                             REGISTRATION STATEMENT
                                      UNDER
                           THE SECURITIES ACT OF 1933

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


<TABLE>
<S>                                <C>                             <C>
            DELAWARE                            2834                     75-2287752
(State or other jurisdiction of    (Primary Standard Industrial       (I.R.S. Employer
 incorporation or organization)     Classification Code Number)    Identification Number)
</TABLE>


                             200 CONSTITUTION DRIVE
                          MENLO PARK, CALIFORNIA 94025
                                 (415) 473-7700

    (Address, including zip code, and telephone number, including area code,
                  of Registrant's principal executive offices)

                                RONALD W. EASTMAN
                      PRESIDENT AND CHIEF EXECUTIVE OFFICER
                                GERON CORPORATION
                             200 CONSTITUTION DRIVE
                          MENLO PARK, CALIFORNIA 94025
                                 (415) 473-7700

   (Name and address, including zip code, and telephone number, including area
                           code, of agent for service)

                                   COPIES TO:
           JOSHUA L. GREEN                            JEROME L. COBEN
         EDGAR B. CALE, III                        SKADDEN, ARPS, SLATE,
          VENTURE LAW GROUP                           MEAGHER & FLOM
         2800 SAND HILL ROAD                      300 SOUTH GRAND AVENUE
    MENLO PARK, CALIFORNIA  94025              LOS ANGELES, CALIFORNIA 90071
           (415) 854-4488                             (213) 687-5000

                   DATE OF COMMENCEMENT OF SALE TO THE PUBLIC:
                                  JULY 31, 1996

      If this Form is filed to register additional securities for an offering
pursuant to Rule 462(b) under the Securities Act, please check the following box
and list the Securities Act registration number of the earlier effective
registration statement for the same offering. [ ] ________.

      If this Form is a post-effective amendment filed pursuant to Rule 462(c)
under the Securities Act, check the following box and list the Securities Act
registration number of the earlier effective registration statement for the same
offering. [ ] ________.

      If delivery of the prospectus is expected to be made pursuant to Rule
434, please check the following box. [ ]

<PAGE>   2
      The Registrant hereby withdraws from registration 375,000 shares of its
Common Stock registered to cover an over-allotment option granted to the
Underwriters, which option was not exercised and has expired. The Registration
Statement is hereby amended, as appropriate, to reflect the expiration of such
option.


                                      -2-

<PAGE>   3

                                   SIGNATURES

      Pursuant to the requirements of the Securities Act of 1933, the Registrant
has duly caused this Post-Effective Amendment No. 1 to Registration Statement on
Form S-1 to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Menlo Park, State of California, on September 19,
1996.

                                    GERON CORPORATION

                                    By:  /s/  Ronald W. Eastman
                                       -----------------------------------------
                                       Ronald W. Eastman
                                       (President and Chief Executive Officer)

      PURSUANT TO THE REQUIREMENTS OF THE SECURITIES ACT OF 1933, THIS
POST-EFFECTIVE AMENDMENT NO. 1 TO REGISTRATION STATEMENT ON FORM S-1 HAS BEEN
SIGNED BY THE FOLLOWING PERSONS IN THE CAPACITIES AND ON THE DATES INDICATED:

           SIGNATURE            TITLE                            DATE

     /s/ RONALD W. EASTMAN*     President, Chief Executive
- ------------------------------  Officer and Director
       Ronald W. Eastman        (Principal Executive         September 19, 1996
                                Officer)                     

    /s/ DAVID L. GREENWOOD*     Chief Financial Officer,
- ------------------------------  Treasurer and Secretary
      David L. Greenwood        (Principal Financial and     September 19, 1996
                                Accounting Officer)          

   /s/ ALEXANDER E. BARKAS*     Director
- ------------------------------
      Alexander E. Barkas                                    September 19, 1996

       /s/ BRIAN H. DOVEY*      Director
- ------------------------------
        Brian H. Dovey                                       September 19, 1996
                                                             
    /s/ CHARLES M. HARTMAN*     Director
- ------------------------------
      Charles M. Hartman                                     September 19, 1996
                                                             
      /s/ THOMAS D. KILEY*      Director
- ------------------------------
        Thomas D. Kiley                                      September 19, 1996
                                                             
  /s/ PATRICK F. LATTERELL*     Director
- ------------------------------
     Patrick F. Latterell                                    September 19, 1996
                                                             
      /s/ ROBERT B. STEIN*      Director
- ------------------------------
        Robert B. Stein                                      September 19, 1996
                                                             
      /s/ MICHAEL D. WEST*      Director
- ------------------------------
        Michael D. West                                      September 19, 1996
                                                             
  *By:/s/ RONALD W. EASTMAN
      ------------------------
      Ronald W. Eastman,                                     September 19, 1996
       Attorney-in-fact