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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2005-05-18</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001158463</issuerCik>
        <issuerName>JETBLUE AIRWAYS CORP</issuerName>
        <issuerTradingSymbol>JBLU</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001187891</rptOwnerCik>
            <rptOwnerName>PETERSON JOEL CLINTON</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>JETBLUE AIRWAYS CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>118-29 QUEENS BLVD.</rptOwnerStreet2>
            <rptOwnerCity>FOREST HILLS</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>11375</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Purchase)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>22.13</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2005-05-18</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>9000</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2005-05-18</value>
                <footnoteId id="F2"/>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2015-05-18</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>9000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The option was granted under the issuer's 2002 Stock Incentive Plan.</footnote>
        <footnote id="F2">The option is immediately exercisable for any or all of the shares underlying the option.  However, any shares purchased under the option will be subject to repurchase by the Issuer, at the lower of the option price paid per share or the fair market value per share, should the reporting person cease service on the Issuer's board of directors prior to vesting in the shares.</footnote>
        <footnote id="F3">The shares subject to the option will vest upon the reporting person's completion of one year of service on the issuer's board of directors.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>Joel Peterson</signatureName>
        <signatureDate>2005-05-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
