With　the　increasing　cross-factory　cooperation　in　manufacturing,　the　communication　between　Industrial　Internet　of　Things　(IIoT)　devices　from　discrete　domains　(e.g.,　indepen-dent　factories)　has　become　common.　Authentication　schemes　are　widely　adopted　to　secure　device-to-device　communications.　However,　most　existing　schemes　directly　use　the　real　identities　of　IIoT　devices　for　communication　and　even　publish　them　onto　a　publicly　available　blockchain.　It　allows　attackers　to　easily　identify　devices,　relate　them　with　specific　factories　owned　them,　and　further　extract　the　factories＇　private　information.　To　address　this　issue,　we　propose　a　privacy-aware　cross-domain　authentication　scheme　for　IIoT　devices　based　on　blockchain.　In　the　proposed　scheme,　IIoT　devices　use　different　pseudonyms　for　each　session　instead　of　their　real　identities　to　maintain　anonymity　and　un-linkability.　Besides,　the　proposed　certificateless　signature　scheme　can　eliminate　the　reliance　on　certificates　that　might　expose　the　ownership　of　devices.　We　also　proposed　an　identity　management　mechanism　to　realize　identity　revocation　and　malicious　device　tracking.　The　security　analysis　and　performance　evaluation　results　show　that　our　scheme　is　feasible　and　efficient　for　cross-domain　authentication.　©　2021　IEEE.