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    <schemaVersion>X0306</schemaVersion>

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    <periodOfReport>2020-07-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001058057</issuerCik>
        <issuerName>MARVELL TECHNOLOGY GROUP LTD</issuerName>
        <issuerTradingSymbol>MRVL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001452385</rptOwnerCik>
            <rptOwnerName>Hu Jean X.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>5488 MARVELL LANE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SANTA CLARA</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>95054</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Financial Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
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            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
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                <transactionShares>
                    <value>1972</value>
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        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F3"/>
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            <transactionDate>
                <value>2020-07-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3105</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3105</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9314</value>
                </sharesOwnedFollowingTransaction>
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            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionTimeliness>
                <value></value>
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                <transactionShares>
                    <value>3866</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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                </underlyingSecurityTitle>
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                    <value>27064</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
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        <derivativeTransaction>
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                <value>2020-07-15</value>
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                <transactionCode>M</transactionCode>
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                <value></value>
            </transactionTimeliness>
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                <transactionShares>
                    <value>3976</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
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                <footnoteId id="F6"/>
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                    <value>Common Shares</value>
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                    <value>3976</value>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>43738</value>
                </sharesOwnedFollowingTransaction>
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    </derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 1628 shares acquired under the Marvell 2000 Employee Stock Purchase Plan on June 5, 2020.</footnote>
        <footnote id="F2">Surrender of shares in payment of tax withholding due as a result of the vesting of restricted stock units (&quot;RSUs&quot;).</footnote>
        <footnote id="F3">Each restricted stock unit represents a contingent right to receive one Marvell Technology Group Ltd. (&quot;Marvell&quot;) common share upon vesting.</footnote>
        <footnote id="F4">The remaining RSUs vest on each of 10/15/2020, 1/15/2021, and 4/15/2021.</footnote>
        <footnote id="F5">The remaining RSUs vest on each of 10/15/2020, 1/15/2021, 4/15/2021, 7/15/2021, 10/15/2021, 1/15/2022 and 4/15/2022.</footnote>
        <footnote id="F6">The remaining RSU's will vest on 10/15/20, 1/15/21, 4/15/21, 7/15/21, 10/15/21, 1/15/22, 4/15/22, 7/15/22, 10/15/22, 1/15/23 and 4/15/23.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Jean Hu by Blair Walters as Attorney-in-Fact</signatureName>
        <signatureDate>2020-07-16</signatureDate>
    </ownerSignature>
</ownershipDocument>
