Binary　hyper-sphere　support　vector　machine　(SVM)　is　a　new　method　for　data　description.　Its　weakness　is　that　the　margin　between　two　classes　of　samples　is　zero　or　an　uncertain　value,　which　affects　the　classifier＇s　generalization　performance　to　some　extent.　So　a　generalized　hyper-sphere　SVM　(GHSSVM)　is　provided　in　this　paper.　By　introducing　the　parameter　n　and　b　(n＞b),　the　margin　which　is　greater　than　zero　may　be　obtained.　The　experimental　results　show　the　proposed　classifier　may　have　better　generalization　performance　and　the　less　experimental　risk　than　the　hyper-sphere　SVM　in　the　references.　©　2008　IEEE.