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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2016-02-23</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001195739</issuerCik>
        <issuerName>NUVEEN NEW YORK AMT-FREE MUNICIPAL INCOME FUND</issuerName>
        <issuerTradingSymbol>NRK</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000831001</rptOwnerCik>
            <rptOwnerName>CITIGROUP INC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>388 GREENWICH STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10013</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Variable Rate Demand Preferred Shares (Series 2)</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>168</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Subsidiary</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The Variable Rate Demand Preferred Shares (&quot;Shares&quot;) reported in Table I represent Shares beneficially owned by Citigroup Global Markets Inc.(&quot;CGMI&quot;). Citigroup Financial Products Inc. (&quot;CFP&quot;) is the sole stockholder of CGMI. Citigroup Global Markets Holdings Inc. (&quot;CGMH&quot;) is the sole stockholder of CFP. Citigroup Inc. is the sole stockholder of CGMH.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Citigroup Inc., By: /s/ Ali L. Karshan, Assistant Secretary</signatureName>
        <signatureDate>2016-02-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
