The　k-means　problem　is　a　classical　combinatorial　optimization　problem　which　has　lots　of　applications　in　many　fields　such　as　machine　learn-ing,　data　mining,　etc.　We　consider　a　variant　of　k-means　problem　in　the　spherical　space,　that　is,　spherical　k-means　problem　with　penalties.　In　the　problem,　it　is　allowable　that　some　nodes　in　the　spherical　space　can　not　be　clustered　by　paying　some　penalty　costs.　Based　on　local　search　scheme,　we　propose　a　(4(11　+　4　root　7)　+　epsilon)-approximation　algorithm　using　singe-swap　oper-ation,　where　E　is　a　positive　constant.