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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2018-05-16</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000878927</issuerCik>
        <issuerName>OLD DOMINION FREIGHT LINE INC/VA</issuerName>
        <issuerTradingSymbol>ODFL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001613364</rptOwnerCik>
            <rptOwnerName>Aaholm Sherry A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O OLD DOMINION FREIGHT LINE, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>500 OLD DOMINION WAY</rptOwnerStreet2>
            <rptOwnerCity>THOMASVILLE</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>27360</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes></footnotes>

    <ownerSignature>
        <signatureName>/s/ Sherry A. Aaholm</signatureName>
        <signatureDate>2018-05-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
