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

    <schemaVersion>X0203</schemaVersion>

    <documentType>3/A</documentType>

    <periodOfReport>2009-10-20</periodOfReport>

    <dateOfOriginalSubmission>2009-10-20</dateOfOriginalSubmission>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001421419</issuerCik>
        <issuerName>AGA Medical Holdings, Inc.</issuerName>
        <issuerTradingSymbol>AGAM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001123639</rptOwnerCik>
            <rptOwnerName>WELSH CARSON ANDERSON &amp; STOWE IX LP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O WELSH, CARSON, ANDERSON &amp; STOWE</rptOwnerStreet1>
            <rptOwnerStreet2>320 PARK AVENUE, SUITE 2500</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</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>29775360</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Series A Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>141209659</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">All shares of Preferred Stock will automatically convert into Common Stock upon consummation of the Issuer's initial public offering.</footnote>
        <footnote id="F2">Includes shares that will be issued at the time of conversion of the Preferred Stock in payment of dividends on such Preferred Stock accrued and unpaid as of that date, assuming an IPO closing date of October 26, 2009 and based on an actual IPO price of $14.50 per share of Common Stock.  The original Form 3 filed by the Reporting Person assumed an IPO price of $15.50 per share.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/David Mintz, Attorney-in-Fact</signatureName>
        <signatureDate>2009-10-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
