The　capacitated　min-k-cut　problem　of　hypergraph　is　the　problem　of　partitioning　the　vertices　into　k　parts,　and　each　part　has　a　different　capacity.　The　objective　is　to　minimize　the　weight　of　cut　hyperedges.　It　is　an　NP-hard　problem　which　is　an　important　problem　with　extensive　applications　to　many　areas,　such　as　VLSI　CAD,　image　segmentation,　etc.　Although　many　heuristic　algorithms　have　been　developed,　to　the　best　of　our　knowledge,　no　approximation　algorithm　is　known　for　such　problem.　We　present　a　local　search　algorithm　for　hypergraph　capacitated　min-k-cut　problem,　using　the　idea　of　complement.　The　algorithm　achieves　a　competitive　approximation　factor　of　1/1+s/2　(k-1),　where　s　is　the　largest　cardinality　of　all　hyperedges.　We　also　extend　the　algorithm　and　get　an　approximate　result　for　hypergraph　capacitated　max-k-cut　problem.　©　2010　IEEE.