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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2010-09-03</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000046640</issuerCik>
        <issuerName>HEINZ H J CO</issuerName>
        <issuerTradingSymbol>HNZ</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000928265</rptOwnerCik>
            <rptOwnerName>PELTZ NELSON</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>280 PARK AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10017</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001345471</rptOwnerCik>
            <rptOwnerName>Trian Fund Management, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>280 PARK AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>41ST FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10017</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>less than 10% owner</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.25 Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2010-09-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3250</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15250</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $.25 Par Value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4863897</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Please see explanation below</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">2010 Director Equity Award.  The shares are held by Mr. Peltz for the benefit of the Trian Entities (as defined in Note 2 below) pursuant to an agreement between Mr. Peltz and Trian Management (as defined in Note 2 below) with respect to the fees received by Mr. Peltz for serving on the Board of Directors of the Issuer.</footnote>
        <footnote id="F2">Trian Fund Management GP, LLC (&quot;Trian Management GP&quot;) is the general partner of Trian Fund Management, L.P (&quot;Trian Management&quot;), which serves as the management company for Trian Partners, L.P. (&quot;Trian Onshore&quot;), Trian Partners Master Fund, L.P. (&quot;Trian Offshore&quot;) and Trian Partners Parallel Fund I, L.P. (&quot;Parallel Fund I&quot; and collectively, the &quot;Trian Entities&quot;).</footnote>
        <footnote id="F3">(FN 2, contd.) Trian Partners General Partner, LLC (&quot;Trian GP LLC&quot;) is the general partner of Trian Partners GP, L.P. (&quot;Trian GP&quot;), which is the general partner of Trian Onshore and Trian Offshore. Trian Partners Parallel Fund I General Partner, LLC (&quot;Parallel Fund I GP LLC&quot;) is the general partner of Parallel Fund I. Mr. Peltz is a member of each of Trian Management GP, Trian GP LLC and Parallel Fund I GP LLC (the &quot;Management Entities&quot;) and therefore is in a position to determine the investment and voting decisions made by the Trian Entities.</footnote>
        <footnote id="F4">(FN 3, contd.) Accordingly, Mr. Peltz may be deemed to indirectly beneficially own (as that term is defined in Rule 13d-3 under the Securities Exchange Act of 1934) the shares beneficially owned by the Management Entities and the Trian Entities.  The Reporting Persons disclaim beneficial ownership of such shares except to the extent of their respective pecuniary interest therein and this report shall not be deemed an admission that the Reporting Persons are the beneficial owner of such securities for purposes of Section 16 or for any other purpose.  Mr. Peltz is a director of the Issuer.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Stuart I. Rosen, Attorney-In-Fact for Nelson Peltz</signatureName>
        <signatureDate>2010-09-08</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>By: Stuart I. Rosen, Attorney-In-Fact for Peter W. May, member of the general partner of Trian Fund Management, L.P.</signatureName>
        <signatureDate>2010-09-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
