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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-03-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000105608</issuerCik>
        <issuerName>WELLS GARDNER ELECTRONICS CORP</issuerName>
        <issuerTradingSymbol>WGA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001330693</rptOwnerCik>
            <rptOwnerName>BRACE JAMES F</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>9500 W 55TH STREET</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE A</rptOwnerStreet2>
            <rptOwnerCity>MCCOOK</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60525-3605</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Ex. VP/CFO/Secretary/Treas.</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock Par Value $1.00</value>
            </securityTitle>
            <transactionDate>
                <value>2013-03-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>2.04</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>101056</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Prior to the transactions reported on this Form 4, Mr. Brace has beneficial ownership of 104,056 shares comprised of 67,205 shares owned and restricted stock awards
representing 36,851 shares. Following the transaction reported on this Form 4, Mr. Brace has beneficial ownership of 101,056 shares, comprised of 64,205 shares owned and
restricted stock awards representing 36,851 shares.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ James F. Brace</signatureName>
        <signatureDate>2013-03-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
