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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2022-08-18</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001034670</issuerCik>
        <issuerName>AUTOLIV INC</issuerName>
        <issuerTradingSymbol>ALV</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001944234</rptOwnerCik>
            <rptOwnerName>LUNDGREN GUSTAV</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O AUTOLIV INC.</rptOwnerStreet1>
            <rptOwnerStreet2>KLARABERGSVIADUKTEN 70, SECTION B7</rptOwnerStreet2>
            <rptOwnerCity>STOCKHOLM</rptOwnerCity>
            <rptOwnerState>V7</rptOwnerState>
            <rptOwnerZipCode>111 64</rptOwnerZipCode>
            <rptOwnerStateDescription>SWEDEN</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>See Exhibit 24- Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ Brian Kelly, as attorney-in-fact</signatureName>
        <signatureDate>2022-08-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
