In the past two decades,many statistical depth functions seemed as powerful exploratory and inferential tools for multivariate data analysis have been presented.In this paper,a new depth function family that meets four properties mentioned in Zuo and Settling(2000)is proposed.Then a classification rule based on the depth function family is proposed.The classification parameter b could be modified according to the type-Ⅰ error α,and the estimator of b has the consistency and achieves the convergence rate n-1/2.With the help of the proper selection for depth family parameter c,the approach for discriminant analysis could minimize the type-Ⅱ error β.A simulation study and a real data example compare the performance of the different discriminant methods.