Big　data　clustering　is　a　fundamental　problem　with　a　vast　number　of　applications.　Due　to　the　increasing　size　of　data,　interests　in　clustering　problems　in　distributed　computation　models　have　increased.　On　the　other　hand,　because　important　decision　making　is　being　automated　with　the　help　of　algorithms,　therefore,　fairness　in　algorithms　has　become　an　especially　important　research　topic.　In　this　work,　we　design　new　distributed　algorithms　for　the　fair　k-center　problem　with　outliers.　Our　main　contributions　are:　(1)　In　the　fair　k-center　problem　with　outliers　setting　we　give　a　4-approximation　ratio　algorithm.　(2)　In　the　distributed　fair　k-center　problem　with　outliers　setting　we　give　a　18-approximation　ratio　algorithm.