<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0304</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2010-11-30</periodOfReport>

    <dateOfOriginalSubmission>2010-12-21</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001364479</issuerCik>
        <issuerName>HERTZ GLOBAL HOLDINGS INC</issuerName>
        <issuerTradingSymbol>HTZ</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000070858</rptOwnerCik>
            <rptOwnerName>BANK OF AMERICA CORP /DE/</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>BANK AMERICA CORPORATE CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>100 N TRYON ST</rptOwnerStreet2>
            <rptOwnerCity>CHARLOTTE</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>28255</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2010-11-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1300</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.7485</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>39183155</value>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
                    <footnoteId id="F9"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See  Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F10"/>
                    <footnoteId id="F11"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">This amendment is being filed to correct the amount of securities beneficially owned following the transactions reported in Table I of the Form 4 filed on December 21, 2010.  Other than as described in footnote 2, there are no other changes from the information originally reported.</footnote>
        <footnote id="F2">This amendment is being filed to include a transaction omitted from Table I of the Form 4 filed on December 21, 2010.  The 1,300 shares disposed of in this transaction were not reflected in the amounts of securities beneficially owned reported on such Form 4.</footnote>
        <footnote id="F3">This Form 4 is being filed by Bank of America Corporation (&quot;BAC&quot; or the &quot;Reporting Person&quot;), a Delaware corporation and bank holding company registered under the Bank Holding Company Act of 1956, on behalf of its subsidiaries.</footnote>
        <footnote id="F4">Transaction executed by the error correction section of Merrill Lynch, Pierce, Fenner &amp; Smith Incorporated (&quot;MLPFS&quot;), a broker-dealer and subsidiary of BAC, to correct errors made in connection with trades made on behalf of clients of MLPFS.</footnote>
        <footnote id="F5">In connection with this transaction, BAC has agreed to voluntarily remit appropriate profits, if any, to the Issuer. BAC disclaims that such transaction is subject to reporting under Section 16(a) or disgorgement under Section 16(b), and this report shall not be deemed an admission that those sections apply to such transaction.</footnote>
        <footnote id="F6">32,187,417 shares are owned directly by ML Global Private Equity Fund, L.P. (&quot;MLGPE&quot;). MLGPE Ltd. is the general partner of MLGPE and is a wholly owned subsidiary of ML Global Private Equity Partners, L.P. (&quot;MLGPEP&quot;), the general partner of which is Merrill Lynch GP, Inc. (&quot;ML GP&quot;), which is a wholly owned subsidiary of Merrill Lynch Group Inc. (&quot;ML Group&quot;), which is a wholly owned subsidiary of Merrill Lynch &amp; Co., Inc. (&quot;ML&amp;Co.&quot;), which is a wholly owned subsidiary of BAC.</footnote>
        <footnote id="F7">3,872,549 shares are owned directly by Merrill Lynch Ventures L.P. 2001 (&quot;MLV LP&quot;), a limited partnership whose general partner is Merrill Lynch Ventures, L.L.C. (&quot;MLV LLC&quot;), a wholly owned subsidiary of ML Group, which is a wholly owned subsidiary of ML&amp;Co.</footnote>
        <footnote id="F8">3,101,137 shares are owned directly by ML Hertz Co-Investor, L.P. (&quot;Hertz Co-Investor LP&quot;), a limited partnership whose general partner is ML Hertz Co-Investor GP, L.L.C. (&quot;Hertz Co-Investor LLC&quot;), whose sole managing member is MLGPE.</footnote>
        <footnote id="F9">22,052 shares are owned by MLPFS.</footnote>
        <footnote id="F10">Each of BAC, ML&amp;Co., MLGPE, MLGPE Ltd., MLGPEP, ML GP, ML Group, MLV LP, MLV LLC, Hertz Co-Investor LP, Hertz Co-Investor LLC, MLPFS and MLGPEI (collectively, the &quot;Reporting Persons&quot;) disclaims beneficial ownership of these securities except to the extent of its pecuniary interest therein.</footnote>
        <footnote id="F11">Pursuant to the Shareholders Agreement dated December 21, 2005, as may be amended from time to time, among Clayton, Dubilier &amp; Rice Fund VII, L.P., CDR CCMG Co-Investor L.P., CD&amp;R Parallel Fund VII, L.P., Carlyle Partners IV, L.P., CP IV Coinvestment L.P., CEP II U.S. Investments, L.P., CEP II Participations S.a.r.l, MLGPE, MLV LP, CMC-Hertz Partners, L.P. and Hertz Co-Investor LP, MLGPE has the right to designate two members to the board of directors of the Issuer. Each of the Reporting Persons other than MLGPE disclaims its possible status as director of the Issuer.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Margaret E. Nelson, Authorized Signatory</signatureName>
        <signatureDate>2012-03-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
