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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-11-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001231908</rptOwnerCik>
            <rptOwnerName>TAGUE JOHN P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>999 VANDERBILT BEACH ROAD</rptOwnerStreet1>
            <rptOwnerStreet2>3RD FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NAPLES</rptOwnerCity>
            <rptOwnerState>FL</rptOwnerState>
            <rptOwnerZipCode>34108</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Options (right to purchase)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>22.75</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-11-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>500000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>500000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>500000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On November 21, 2014, the Reporting Person was issued:  (1) an option to acquire 500,000 shares of common stock of the Issuer (the &quot;transition options&quot;) that will vest on December 31, 2015 if the Reporting Person develops and presents a business plan by December 31, 2015 that is approved by the Board of Directors, and a management team that is reasonably acceptable to the Board is in place by June 30, 2015, subject to the Reporting Person's continued employment on the vesting date, which will expire no later than December 31, 2019; and (2) an option to acquire 500,000 shares of common stock of the Issuer that will vest on December 31, 2017, subject to the satisfaction of revenue efficiency metrics in respect of the period from 2015-2017 to be developed by the Compensation Committee of the Board with input from the Reporting Person, and the Reporting Person continued employment on the vesting date, which will expire no later than June 30, 2020.</footnote>
        <footnote id="F2">On November 10, 2015, the performance criteria for the transition options were satisfied and the transition options will vest on December 31, 2015 if the Reporting Person continues to be employed by the Issuer on such date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>William Langston, By Power of Attorney on behalf of John P. Tague</signatureName>
        <signatureDate>2014-11-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
