In　this　paper,　we　consider　the　uniform　capacitated　k-means　problem　(UC-k-means),　an　extension　of　the　classical　k-means　problem　(k-means)　in　machine　learning.　In　the　UC-k-means,　we　are　given　a　set　D　of　n　points　in　d-dimensional　space　and　an　integer　k.　Every　point　in　the　d-dimensional　space　has　an　uniform　capacity　which　is　an　upper　bound　on　the　number　of　points　in　D　that　can　be　connected　to　this　point.　Every　twopoint　pair　in　the　space　has　an　associated　connecting　cost,　which　is　equal　to　the　square　of　the　distance　between　these　two　points.　We　want　to　find　at　most　k　points　in　the　space　as　centers　and　connect　every　point　in　D　to　some　center　without　violating　the　capacity　constraint,　such　that　the　total　connecting　costs　is　minimized.　Based　on　the　technique　of　local　search,　we　present　a　bi-criteria　approximation　algorithm,　which　has　a　constant　approximation　guarantee　and　violates　the　cardinality　constraint　within　a　constant　factor,　for　the　UC-k-means.