The　clustering　problem　of　big　data　in　the　era　of　artificial　intelligence　has　been　widely　studied.　Because　of　the　huge　amount　of　data,　distributed　algorithms　are　often　used　to　deal　with　big　data　problems.　The　distributed　computing　model　has　an　attractive　feature:　it　can　handle　massive　datasets　that　cannot　be　put　into　the　main　memory.　On　the　other　hand,　since　many　decisions　are　made　automatically　by　machines　in　today＇s　society,　algorithm　fairness　is　also　an　important　research　area　of　machine　learning.　In　this　paper,　we　study　two　fair　clustering　problems:　the　centralized　fair　k-center　problem　with　outliers　and　the　distributed　fair　k-center　problem　with　outliers.　For　these　two　problems,　we　have　designed　corresponding　constant　approximation　ratio　algorithms.　The　theoretical　proof　and　analysis　of　the　approximation　ratio,　and　the　running　space　of　the　algorithm　are　given.