Abstract: Working set selection is an important step in the sequential minimal optimization (SMO) type methods for training support vector machine (SVM). However, the feasible direction strategy for selecting working set may degrade the performance of the kernel cache maintained in standard SMO. In this paper, an improved strategy for selecting working set applied in SMO is presented to handle such difficulties based on the decrease of objective function corresponding to second order information. The new strategy takes into consideration both iteration times and kernel cache performance related to the selection of working set in order to improve the efficiency of the kernel cache, which leads to reduction of the number of kernel evaluation of the algorithm as a whole. As a result, the training efficiency of the new method upgrades greatly compared with the older version. On the other hand, the SMO with the new strategy of working set selection is guaranteed to converge to an optimal solution in theory. It is shown in the experiments on the well-known data sets that the proposed method is remarkably faster than the standard SMO. The more complex the kernel is, the higher the dimensional spaces are, and the relatively smaller the cache is, the greater the improvement is.