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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2017-01-01</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001383441</issuerCik>
        <issuerName>AllianzGI Equity &amp; Convertible Income Fund</issuerName>
        <issuerTradingSymbol>NIE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001694100</rptOwnerCik>
            <rptOwnerName>Thompson Kathleen C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1633 BROADWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Affiliated Person</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>Ms. Thompson is a member of the Executive Committee of Allianz Global Investors U.S. Holdings LLC, the body that performs executive oversight functions for Allianz Global Investors U.S. LLC, the Issuer's investment manager. Exhibit List: Exhibit 24, Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ Thomas J. Fuccillo</signatureName>
        <signatureDate>2017-01-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
