The　spherical　k-means　problem　(SKMP)　is　an　important　variant　of　the　k-means　clustering　problem　(KMP).　In　this　paper,　we　consider　the　SKMP,　which　aims　to　divide　the　n　points　in　a　given　data　point　set　S　into　k　clusters　so　as　to　minimize　the　total　sum　of　the　cosine　dissimilarity　measure　from　each　data　point　to　their　respective　closest　cluster　center.　Our　main　contribution　is　to　design　an　expected　constant　approximation　algorithm　for　the　SKMP　by　integrating　the　seeding　algorithm　for　the　KMP　and　the　local　search　technique.　By　utilizing　the　structure　of　the　clusters,　we　further　obtain　an　improved　LocalSearch++　algorithm　involving　epsilon　k　local　search　steps.