Spherical　k-means　clustering　as　a　known　NP-hard　variant　of　the　k-means　problem　has　broad　applications　in　data　mining.　In　contrast　to　k-means,　it　aims　to　partition　a　collection　of　given　data　distributed　on　a　spherical　surface　into　k　sets　so　as　to　minimize　the　within-cluster　sum　of　cosine　dissimilarity.　In　the　paper,　we　introduce　spherical　k-means　clustering　with　penalties　and　give　a　2max{2,M}(1+M)(lnk+2)-approximation　algorithm.　Moreover,　we　prove　that　when　against　spherical　k-means　clustering　with　penalties　but　on　separable　instances,　our　algorithm　is　with　an　approximation　ratio　2max{3,M+1}　with　high　probability,　where　M　is　the　ratio　of　the　maximal　and　the　minimal　penalty　cost　of　the　given　data　set.