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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-04-09</periodOfReport>

    <issuer>
        <issuerCik>0000815097</issuerCik>
        <issuerName>CARNIVAL CORP</issuerName>
        <issuerTradingSymbol>CCL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001489421</rptOwnerCik>
            <rptOwnerName>BAND SIR JONATHON</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O CARNIVAL CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>3655 N.W. 87TH AVENUE</rptOwnerStreet2>
            <rptOwnerCity>MIAMI</rptOwnerCity>
            <rptOwnerState>FL</rptOwnerState>
            <rptOwnerZipCode>33178</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-04-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>14090</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>33328.905</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-04-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2818</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12.42</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>36146.905</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Issued pursuant to the Carnival Corporation 2020 Stock Plan. The restriction on the shares lapses on the third anniversary of the grant date.</footnote>
        <footnote id="F2">The Board of Directors approved a value of $175,000 to be awarded to the reporting person in the form of restricted shares. The number of shares was determined by dividing this value by the closing price of a share of Carnival Corporation common stock on April 9, 2020, then rounding down to the nearest whole share.</footnote>
        <footnote id="F3">The grant, which reflects the reporting person voluntarily deferring their Board of Director retainer and committee fees for April to June 2020 in the form of restricted shares as described in FN4, was approved by the Compensation Committee. The number of shares was determined by dividing the deferred retainer and committees fees by the closing price of a share of Carnival Corporation common stock on April 9, 2020, then rounding down to the nearest whole share.</footnote>
        <footnote id="F4">Issued pursuant to the Carnival Corporation 2020 Stock Plan. The restriction on the shares lapses on February 12, 2021.</footnote>
        <footnote id="F5">Includes shares acquired pursuant to the dividend reinvestment feature of the reporting person's brokerage account.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Sir Jonathon Band</signatureName>
        <signatureDate>2020-04-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
