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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-02-26</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000921738</issuerCik>
        <issuerName>PENN NATIONAL GAMING INC</issuerName>
        <issuerTradingSymbol>PENN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001211342</rptOwnerCik>
            <rptOwnerName>CARLINO PETER M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>825 BERKSHIRE BLVD SUITE 200</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WYOMISSING</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>19610</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Chairman Emeritus</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-02-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>25336</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>786826</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-02-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>210442</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4520841</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trusts</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Shares acquired by Peter M. Carlino as a beneficiary under the Carlino Family Trust.</footnote>
        <footnote id="F2">Shares distributed to all beneficiaries under the Carlino Family Trust.</footnote>
        <footnote id="F3">Includes 365,212 shares owned by a residuary trust for the benefit of Peter D. Carlino and Peter D. Carlino's children. The reporting person is a trustee of the residuary trust with shared voting and investment power. The reporting person disclaims beneficial ownership of the shares owned by the residuary trust, except to the extent to of his pecuniary interest therein, and this report should not be deemed an admission the reporting person is the beneficial owner of such securities for purposes of Section 16 or any other purpose.</footnote>
        <footnote id="F4">Includes 4,155,269 shares held by the Carlino Family Trust. The reporting person is a trustee of the trust with shared voting and investment power. The reporting person disclaims beneficial ownership of the shares owned by the trust, except to the extent of his pecuniary interest therein, and this report should not be deemed an admission that the reporting person is the beneficial owner of such securities for purposes of Section 16 or any other purpose.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Elliot Hoops as attorney-in-fact for Peter M. Carlino</signatureName>
        <signatureDate>2020-02-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
