Hard-capacitated　k-means　(HCKM)　is　one　of　the　fundamental　problems　remaining　open　in　combinatorial　optimization　and　engineering.　In　HCKM,　one　is　required　to　partition　a　given　n-point　set　into　k　disjoint　clusters　with　known　capacity　so　as　to　minimize　the　sum　of　within-cluster　variances.　It　is　known　to　be　at　least　APX-hard,　and　most　of　the　work　on　it　has　been　done　from　a　meta　heuristic　or　bi-criteria　approximation　perspective.　To　the　best　our　knowledge,　no　constant　approximation　algorithm　or　existence　proof　of　such　an　algorithm　is　known.　As　our　main　contribution,　we　propose　an　FPT(k)　approximation　algorithm　with　constant　performance　guarantee　for　HCKM　in　this　paper.