Recently,　there　has　been　a　surge　of　interest　in　incorporating　fairness　aspects　into　classical　clustering　problems.　In　this　paper,　we　consider　adding　fairness　constraints　to　k-center　clustering.　We　use　points　with　different　colors　to　present　individuals　in　distinct　groups,　the　difference　with　the　classic　k-　center　clustering　is　that　we　try　to　constrain　the　number　of　centers　selected　from　each　group　so　that　we　can　achieve　the　goal　to　guarantee　the　fairness.　To　solve　this　problem,　Kleindessner　et　al.　proposed　a　(5　+　ϵ)-approximation　algorithm　in　2019.　So　far,　the　best　algorithm　to　solve　this　problem　is　proposed　by　Jones　et　al.,　whose　approximation　ratio　reached　3.　The　main　contribution　of　this　paper　is:　for　fair　k-center　clustering,　we　propose　a　key　set　with　special　property　and　prove　that　there　exists　a　structure　for　2-approximation　solution　when　the　data　set　is　divided　into　two　groups.　©　2023　IEEE.