Abstract: HSMC-SVM is a kind of high-speed multi-class SVM with direct mode, and it is appropriate for the situation having lots of categories. Because working set selection of SMO algorithm is based on experience, HSMC-SVM would converge slowly trained with SMO. For accelerating the convergence process of HSMC-SVM, a new approach of working set selection based on second order approximation is proposed. At the same time, shrinking strategy is used too. The numeric experiments show that these measures can speed up the convergence process of HSMC-SVM efficiently. The convergence process of HSMC-SVM is even shorter than these composed multi-class SVMs trained with libsvm. Hence, HSMV-SVM based on second order approximation is very appropriate for the situation that classification category is more and the number of training samples is large.