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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2010-09-10</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>2010-09-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>700000</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>46.8943</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4163897</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>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.25 Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2010-09-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>400000</value>
                    <footnoteId id="F5"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>46.7814</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3763897</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>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $.25 Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2010-09-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>519914</value>
                    <footnoteId id="F6"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>46.771</value>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3243983</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>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, $.25 Par Value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15250</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The price shown in Column 4 is a weighted average sale price. The price range for the sales is $46.725 to $46.985. The reporting person undertakes to provide upon request by the staff of the Securities and Exchange Commission, the Issuer or a security holder of the Issuer, full information regarding the number of shares sold at each separate price.</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>
        <footnote id="F5">The price shown in Column 4 is a weighted average sale price. The price range for the sales is $46.50 to $47.075. The reporting person undertakes to provide upon request by the staff of the Securities and Exchange Commission, the Issuer or a security holder of the Issuer, full information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F6">The price shown in Column 4 is a weighted average sale price. The price range for the sales is $46.60 to $46.90. The reporting person undertakes to provide upon request by the staff of the Securities and Exchange Commission, the Issuer or a security holder of the Issuer, full information regarding the number of shares sold at each separate price.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Stuart I. Rosen, Attorney-In-Fact for Nelson Peltz</signatureName>
        <signatureDate>2010-09-14</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>2010-09-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
