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

    <schemaVersion>X0202</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2005-06-23</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001301508</issuerCik>
        <issuerName>KKR Financial Corp</issuerName>
        <issuerTradingSymbol>KFN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001074607</rptOwnerCik>
            <rptOwnerName>ALDINGER WILLIAM F III</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O KKR FINANCIAL CORP.</rptOwnerStreet1>
            <rptOwnerStreet2>FOUR EMBARCADERO CENTER, SUITE 2050</rptOwnerStreet2>
            <rptOwnerCity>SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94111</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>

    <remarks>No securities owned.</remarks>

    <ownerSignature>
        <signatureName>William F. Aldinger</signatureName>
        <signatureDate>2005-06-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
