<?xml version="1.0" encoding="US-ASCII"?>
<!-- DFIN New ActiveDisclosure (SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date :2023-01-04T15:48:21.7565+00:00 -->
<!-- Copyright (c) 2023 Donnelly Financial Solutions, Inc. All Rights Reserved. -->
<xsd:schema targetNamespace="http://www.geron.com/20230104" attributeFormDefault="unqualified" elementFormDefault="qualified" xmlns:enum2="http://xbrl.org/2020/extensible-enumerations-2.0" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:us-gaap="http://fasb.org/us-gaap/2022" xmlns:dei="http://xbrl.sec.gov/dei/2022" xmlns:gern="http://www.geron.com/20230104" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:xlink="http://www.w3.org/1999/xlink">
  <xsd:import schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd" namespace="http://www.xbrl.org/2003/instance"/>
  <xsd:import schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd" namespace="http://www.xbrl.org/2003/linkbase"/>
  <xsd:import schemaLocation="http://www.xbrl.org/2005/xbrldt-2005.xsd" namespace="http://xbrl.org/2005/xbrldt"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/dei/2022/dei-2022.xsd" namespace="http://xbrl.sec.gov/dei/2022"/>
  <xsd:import schemaLocation="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd" namespace="http://fasb.org/us-gaap/2022"/>
  <xsd:annotation>
    <xsd:appinfo>
      <link:linkbaseRef xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="gern-20230104_lab.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" xlink:title="Labels link" xlink:type="simple"/>
      <link:linkbaseRef xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="gern-20230104_pre.xml" xlink:role="http://www.xbrl.org/2003/role/presentationLinkbaseRef" xlink:title="Presentation link" xlink:type="simple"/>
      <link:roleType roleURI="http://www.geron.com/20230104/taxonomy/role/Cover" id="Cover">
        <link:definition>100000 - Document - Cover</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
    </xsd:appinfo>
  </xsd:annotation>
</xsd:schema>
