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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-01-20</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000039368</issuerCik>
        <issuerName>FULLER H B CO</issuerName>
        <issuerTradingSymbol>FUL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001382452</rptOwnerCik>
            <rptOwnerName>Happe Michael J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1200 WILLOW LAKE BOULEVARD</rptOwnerStreet1>
            <rptOwnerStreet2>P.O. BOX 64683</rptOwnerStreet2>
            <rptOwnerCity>ST. PAUL</rptOwnerCity>
            <rptOwnerState>MN</rptOwnerState>
            <rptOwnerZipCode>55164-0683</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes></footnotes>

    <remarks>No securities are beneficially owned by Mr. Happe.</remarks>

    <ownerSignature>
        <signatureName>/s/ Timothy J. Keenan, Attorney-in-Fact</signatureName>
        <signatureDate>2021-01-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
