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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2009-03-31</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></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10017</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</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>2008-03-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>35019</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.06</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6484028</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Please see explanation below</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $.25 Par Value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents a distribution to an investor in a parent entity of Trian Partners Parallel Fund II, L.P. in connection with the expiration of the applicable lock-up period.</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 (i) the management company for Trian Partners, L.P. (&quot;Trian Onshore&quot;), Trian Partners Master Fund, L.P. (&quot;Trian Offshore&quot;), Trian Partners Parallel Fund I, L.P. (&quot;Parallel Fund I&quot;), Trian Partners Parallel Fund II, L.P. (&quot;Parallel Fund II&quot;) and Trian SPV (SUB) I, L.P. (&quot;Trian SPV&quot; and collectively, the &quot;Trian Entities&quot;) and (ii) the investment manager for a separate account owned by TCMG-MA, LLC (the &quot;Separate Account&quot;). Trian Management has full discretion and authority to make all investment and voting decisions in respect of the Separate Account.</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, Trian Offshore and Trian SPV. Trian Partners Parallel Fund I General Partner, LLC (&quot;Parallel Fund I GP LLC&quot;) is the general partner of Parallel Fund I. Trian Partners Parallel Fund II General Partner, LLC (&quot;Parallel Fund II GP LLC&quot;) is the general partner of Trian Partners Parallel Fund II GP, L.P. (&quot;Parallel Fund II GP&quot;), which is the general partner of Parallel Fund II. Each of Trian Management GP, Trian GP LLC, Parallel Fund I GP LLC and Parallel Fund II GP LLC (the &quot;Management Entities&quot;) is controlled by Nelson Peltz, who therefore is in a position to determine the investment and voting decisions made by the Trian Entities and the Separate Account.</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, the Trian Entities and the Separate Account. Mr. Peltz disclaims beneficial ownership of such shares except to the extent of his 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>
        <footnote id="F5">Mr. Peltz and Trian Management disclaim beneficial ownership of all such shares except to the extent of their respective pecuniary interests 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.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By: Stuart I. Rosen, Attorney-In-Fact for Nelson Peltz</signatureName>
        <signatureDate>2009-04-01</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>2009-04-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
