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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-09-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001603600</rptOwnerCik>
            <rptOwnerName>Kortuem Franz-Josef</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O AUTOLIV, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>KLARABERGSVIADUKTEN 70, SECTION B7</rptOwnerStreet2>
            <rptOwnerCity>STOCKHOLM</rptOwnerCity>
            <rptOwnerState>V7</rptOwnerState>
            <rptOwnerZipCode>SE-111 64</rptOwnerZipCode>
            <rptOwnerStateDescription>SWEDEN</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-09-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4.4066</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4.4066</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>613.802</value>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each restricted stock unit (RSU) represents a contingent right to receive one share of ALV common stock.</footnote>
        <footnote id="F2">Dividend equivalent rights accrued in the form of additional RSUs to RSUs granted on May 8, 2018.  Per the award agreement, cash dividends with a record date on or after the grant date and paid on or before the vesting date yield additional RSUs subject to the same vesting schedule as the underlying RSUs.</footnote>
        <footnote id="F3">The RSUs vest and convert to shares in one installment on the earlier of (a) the date of ALV's 2019 annual stockholder meeting, or (b) the one-year anniversary of May 8, 2018.</footnote>
        <footnote id="F4">As reported in the Registration Statement on Form 10 filed by Veoneer, Inc. (&quot;VNE&quot;) with the SEC, in connection with the distribution by ALV of 100% of the outstanding shares of common stock of VNE on a pro rata basis to ALV stockholders on June 29, 2018 (the &quot;Spin-off&quot;), stock-based awards granted by ALV prior to the Spin-off were converted into adjusted stock-based awards relating to both shares of ALV and VNE common stock.</footnote>
        <footnote id="F5">(Continued from footnote 4) With certain limited exceptions, the adjusted awards are subject to the same or equivalent vesting conditions and other terms that applied to the applicable original ALV award immediately before the Spin-off. For each holder of an RSU, 50% of the outstanding stock award value, as calculated immediately prior to the spin-off, was converted to an RSU of VNE, and 50% to an RSU of ALV, with an adjustment to the number of shares as required to preserve the value inherent in the stock award before and after the distribution.  The conversion and adjustment described herein is referred to as the &quot;Spin-off Conversion and Adjustment.&quot;</footnote>
        <footnote id="F6">The number of RSUs held following the Spin-off Conversion and Adjustment.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Zachariah Miller, as attorney-in-fact</signatureName>
        <signatureDate>2018-09-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
