At present sequential minimal optimization (SMO) is one of the most popular and efficient training algorithms for support vector machines (SVM), especially for large-scale problems. A novel strategy for selecting working sets applied in SMO is presented in the paper. Based on the original feasible direction method, the new strategy also takes the efficiency of kernel cache maintained in SMO into consideration. It is shown in the experiments on the well-known data sets that computation of the kernel function and training time is reduced greatly, especially for the problems with many samples and support vectors.