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

    <schemaVersion>X0203</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2011-07-18</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001515173</issuerCik>
        <issuerName>New Mountain Finance AIV Holdings Corp</issuerName>
        <issuerTradingSymbol>NONE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001515175</rptOwnerCik>
            <rptOwnerName>New Mountain Investments III, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O NEW MOUNTAIN CAPITAL, L.L.C.</rptOwnerStreet1>
            <rptOwnerStreet2>787 7TH AVENUE, 48TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</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>0001407718</rptOwnerCik>
            <rptOwnerName>New Mountain Capital, L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>787 7TH AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>48TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Former 10% Owner</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001515174</rptOwnerCik>
            <rptOwnerName>New Mountain Guardian AIV, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O NEW MOUNTAIN CAPITAL, L.L.C.</rptOwnerStreet1>
            <rptOwnerStreet2>787 SEVENTH AVENUE, 48TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>100</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Note</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">New Mountain Guardian AIV, L.P. (&quot;Guardian AIV&quot;) directly owns 100 shares of common stock of New Mountain Finance AIV Holdings Corporation (&quot;AIV Holdings&quot;).  New Mountain Investments III, L.L.C. is the general partner of Guardian AIV, and may be deemed to beneficially own these shares.  New Mountain Capital, L.L.C. is the investment adviser to Guardian AIV, and may be deemed to beneficially own these shares.  New Mountain Investments III, L.L.C. and New Mountain Capital, L.L.C. each disclaim beneficial ownership of these shares except to the extent of their pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Adam Weinstein as Authorized Signatory of New Mountain Investments III, L.L.C.</signatureName>
        <signatureDate>2011-07-13</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Adam Weinstein as Authorized Signatory of New Mountain Capital, L.L.C.</signatureName>
        <signatureDate>2011-07-13</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Adam Weinstein as Authorized Signatory of New Mountain Guardian AIV, L.P.</signatureName>
        <signatureDate>2011-07-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
