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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-03-11</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000739608</issuerCik>
        <issuerName>PENFORD CORP</issuerName>
        <issuerTradingSymbol>PENX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001249317</rptOwnerCik>
            <rptOwnerName>RANDALL JOHN R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PENFORD CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>7094 S. REVERE PARKWAY</rptOwnerStreet2>
            <rptOwnerCity>CENTENNIAL</rptOwnerCity>
            <rptOwnerState>CO</rptOwnerState>
            <rptOwnerZipCode>80112-3932</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Vice Pres.</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-03-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>33175</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>19.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>401(k) plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>5.65</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-03-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>75000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2013-01-26</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2019-01-26</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>75000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>17.07</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-03-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>20000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2009-08-28</value>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2015-08-28</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>20000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Common Stock and derivative securities of Penford Corporation (&quot;Issuer&quot;) were disposed of pursuant to the transactions contemplated by the Agreement and Plan of Merger among Issuer, Ingredion Incorporated (&quot;Acquiror&quot;), and Prospect Sub, Inc., dated as of October 14, 2014 (the &quot;Merger Agreement&quot;).  Upon closing of the transactions contemplated by the Merger Agreement (the &quot;Effective Time&quot;), Issuer became a wholly owned subsidiary of Acquiror, and each share of Common Stock of Issuer, including outstanding restricted stock which by its terms became fully vested at the Effective Time, was converted into the right to receive $19 in cash, and each stock option relating to the Common Stock of Issuer (a &quot;Stock Option&quot;) was converted into the right to receive cash equal to the excess if any, of $19 over the per share exercise price of such Stock Option, less any applicable tax withholding.</footnote>
        <footnote id="F2">The option becomes exercisable in three equal installments beginning on the first anniversary from date of grant; the first anniversary is indicated above as the Date Exercisable.</footnote>
        <footnote id="F3">The option becomes exercisable in four equal installments beginning on the first anniversary from date of grant; the first anniversary is indicated above as the Date Exercisable.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Margaret Von der Schmidt as Attorney-in-Fact</signatureName>
        <signatureDate>2015-03-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
