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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2005-12-19</periodOfReport>

    <dateOfOriginalSubmission>2005-12-21</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001051431</issuerCik>
        <issuerName>HORIZON OFFSHORE INC</issuerName>
        <issuerTradingSymbol>HOFF</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000949119</rptOwnerCik>
            <rptOwnerName>MILLER LLOYD I III</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4550 GORDON DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NAPLES</rptOwnerCity>
            <rptOwnerState>FL</rptOwnerState>
            <rptOwnerZipCode>34102</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>52414970</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>20452345</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Milfam II L.P.</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>39544075</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Lloyd I. Miller, III, Trust A-4</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>305468</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Lloyd I. Miller, III, custodian under Florida UGMA for Alexandra B. Miller</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>706492</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Milfam LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>305468</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Lloyd I. Miller, III, Trustee, GST f/b/o Lloyd I. Miller</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>305468</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Lloyd I. Miller, III, Trustee, GST f/b/o Catherine C. Miller</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1946164</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Marli B. Miller Managed Account</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13869481</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Lloyd I. Miller, III, Trust C</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Subordinated Convertible Note due 3/31/2010</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.38</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2005-12-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1535009</value>
                    <footnoteId id="F6"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2005-12-19</value>
            </exerciseDate>
            <expirationDate>
                <value>2006-02-26</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4039497</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1535009</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F7"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Milfam I L.P.</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On December 9, 2005, Milfam I L.P. transferred 3,635,734 shares to the following entities (the &quot;Milfam Transfer&quot;):  (i) 31,819 shares to Miller personally, (ii) 1,865,219 to Trust A-4, (iii) 36,490 shares to Milfam LLC, (iv) 33,082 shares to Marli Miller Managed Account and (v) 1,669,124 shares to Milgrat I STAR.  The Milfam Transfer was exempt from Seciton 16 by virtue of Rule 16a-13 of the Securities Exchange Act of 1934, as amended (the &quot;Exchange Act&quot;), because the transaction constituted a mere change in the form of the beneficial ownership of the reporting person without changing the Reporting Person's pecuniary interest therein.</footnote>
        <footnote id="F2">On December 16, 2005, Milgrat I STAR transferred 17,084,585 shares to the following entities (the &quot;Milgrat Transfer&quot;):  (i) 13,869,481 to Trust C, (ii) 1,607,552 to Miller personally, and (iIi) 1,607,552 to Marli Miller Managed Account.  The Milgrat Transfer was exempt from Seciton 16 by virtue of Rule 16a-13 of the Exchange Act, because the transaction constituted a mere change in the form of the beneficial ownership of the reporting person without changing the Reporting Person's pecuniary interest therein.</footnote>
        <footnote id="F3">This Form 4 hereby amends and restates the prior Form 4 filed on December 21, 2005 in its entirety.</footnote>
        <footnote id="F4">The reporting person disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein.  This filing shall not be deemed an admission that the reporting person is, for purposes of Section 16 or otherwise, the beneficial owner of any securities covered by this filing.</footnote>
        <footnote id="F5">On December 19, 2005, Milfam I L.P. acquired a Subordinated Convertible Note due March 31, 2010 (the &quot;Note&quot;) in the principal amount of $1,535,009.  The Note was acquired in connection with that certain Exchange Agreement dated December 19, 2005, by and between Milfam I. L.P. and the Issuer (the &quot;Exchange&quot;) whereby Milfam I L.P. exchanged in the aggregate $1,535,009 of the Issuer's 8% Subordinated Secured Notes due March 31, 2010 for the Note.</footnote>
        <footnote id="F6">The principal amount of Subordinated Convertible Note acquired in connection with the Exchange was $1,535,009.</footnote>
        <footnote id="F7">The prior Form 4 being amended hereto incorrectly stated the amount of derivative securities beneficially owned of Subordinated Convertible Note was $4,039,497 when in fact such amount was $1,535,009.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ David J. Hoyt
Attorney-in-fact</signatureName>
        <signatureDate>2005-12-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
