In　this　paper,　we　consider　the　spherical　k-means　problem　with　penalties,　a　robust　model　of　spherical　clusterings　that　requires　identifying　outliers　during　clustering　to　improve　the　quality　of　the　solution.　Each　outlier　will　incur　a　specified　penalty　cost.　In　this　problem,　one　should　detect　the　outliers　and　propose　a　k-clustering　for　the　given　data　set　so　as　to　minimize　the　sum　of　the　clustering　and　penalty　costs.　As　our　main　contribution,　we　present　a　(16　+　8　root　3)-approximation　via　single-swap　local　search　and　an　(8　+　2　root　7　+　??)-approximation　via　multi-swap　local　search.