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A new model of multi-class support vector machine with parameter v (v-MC-SVM) is proposed firstly based on v-SVM. Existence of optimal solutions and dual problem of v-MC-SVM are also given. Because the constraints of v-MC-SVM are too complicated, one-class SVM problem is given by adding bm to the objective function of v-MC-SVM and employing the Kesler's construction which simplify the original problem. The optimal solutions of one-class SVM problem are unchanged when its constraint eT Â¿ Â¿ v is replaced with eTÂ¿ = v. Numerical testing results show that the speed of v-MC-SVM algorithm is faster than that of QP-MC-SVM algorithm under the same accuracy rate.