Abstract: Hyper-sphere support vector machine is an important method for unbalanced classification which is an important issue in biomedical engineering such as tongue image classification in traditional chinese medicine. By introducing the other kind of samples, one class support vector domain description classifier is modified to the binary hyper-sphere classifier to improve its generalization performance. However, among the methods in the present references, it is proved that the solution of margin between two classes of samples is uncertain when there is no support vector in one class samples from the point of the optimal solution in this paper. Meantime, the margin between two classes is proved to be zero when there is at least one normal support vector in each kind of samples. The generalization performance is poor if the margin is an uncertain value or it equals to zero to some extent. To improve the right classification rate of the samples, a generalized hyper-sphere SVM is proposed by introducing the parameter n and b （n>b） and the margin which is greater than zero may be acquired, which balances the volume of the hyper-sphere, margin and the experimental error. Theory analysis and experimental results show that the proposed algorithm has better generalization performance and less experimental risk.