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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-07-03</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000070487</issuerCik>
        <issuerName>NATIONAL RESEARCH CORP</issuerName>
        <issuerTradingSymbol>NRC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001579448</rptOwnerCik>
            <rptOwnerName>K/I/E/Trust Under Agreement 3/9/09</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>BESSEMER TRUST COMPANY OF DELAWARE, N.A.</rptOwnerStreet1>
            <rptOwnerStreet2>1007 N. ORANGE ST., SUITE 1450</rptOwnerStreet2>
            <rptOwnerCity>WILMINGTON</rptOwnerCity>
            <rptOwnerState>DE</rptOwnerState>
            <rptOwnerZipCode>19801</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001579075</rptOwnerCik>
            <rptOwnerName>Endacott Kent E.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>WOODS &amp; AITKEN LLP</rptOwnerStreet1>
            <rptOwnerStreet2>301 S. 13TH ST., SUITE 500</rptOwnerStreet2>
            <rptOwnerCity>LINCOLN</rptOwnerCity>
            <rptOwnerState>NE</rptOwnerState>
            <rptOwnerZipCode>68508</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</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>2018-07-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1305</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>38.0001</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5729418</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-07-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6414</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>38.0039</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5723004</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The reported transaction was effected pursuant to a Rule 10b5-1 trading plan adopted by the reporting person on May 21, 2018.</footnote>
        <footnote id="F2">The price reported in Column 4 is a weighted average price.  The shares were sold in multiple transactions at prices ranging from $38.00 to $38.075, inclusive.  The Reporting Person undertakes to provide National Research Corp. (the &quot;Company&quot;), any security holder of the Company, or the staff of the Securities &amp; Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range set forth herein.</footnote>
        <footnote id="F3">The price reported in Column 4 is a weighted average price.  The shares were sold in multiple transactions at prices ranging from $38.00 to $38.10, inclusive.  The Reporting Person undertakes to provide the Company, any security holder of the Company, or the staff of the Securities &amp; Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range set forth herein.</footnote>
    </footnotes>

    <remarks>This Form 4 is being filed by the K/I/E/Trust Under Agreement 3/9/09, f/k/a Michael and Karen Hays Grandchildren's Trust Dated March 9, 2009, and by Kent E. Endacott, as Special Holdings Direction Adviser under the K/I/E/Trust Under Agreement 3/9/09.</remarks>

    <ownerSignature>
        <signatureName>/s/ Russell E. Ryba, Attorney-in-Fact for Kent E. Endacott, as Special Holdings Direction Adviser</signatureName>
        <signatureDate>2018-07-06</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Russell E. Ryba, Attorney-in-Fact for Kent E. Endacott, Special Holdings Direction Adviser under the K/I/E/Trust Under Agreement 3/9/09</signatureName>
        <signatureDate>2018-07-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
