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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-05-18</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001051627</issuerCik>
        <issuerName>AXT INC</issuerName>
        <issuerTradingSymbol>AXTI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001078582</rptOwnerCik>
            <rptOwnerName>YOUNG MORRIS S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4281 TECHNOLOGY DR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>FREMONT</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94538</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-05-18</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.18</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1621019</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">This total includes 518,806 shares of common stock held by the Reporting Person and the Young Family Trust for which the Reporting Person serves as trustee; 218,113 shares of common stock held by the Morris S. S. Young 2016 Annuity Trust for which the Reporting Person serves as trustee; 183,617 shares of common stock held by the Vicke Young 2016 Annuity Trust for which the Reporting Person serves as trustee; In 2019, two additional GRATS were established with 350,000 shares each for which the Reporting Person serves as trustee; and 483 shares of common stock held by the Morris Young Family Ltd. Partnership. This total also corrects a clerical error in the Reporting Person's previous Form 4 The Reporting Person disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and this report shall not be deemed an admission that the Reporting Person is the beneficial owner of the securities for purposes of Section 16 or for any other purpose</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Morris S Young, by power of attorney</signatureName>
        <signatureDate>2020-05-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
