Abstract: It has been pointed out by Poggio that the b term in support vector machine (SVM) is to guarantee the positive definitiveness of kernel and b is not needed if the used kernel is positive definite. To testify the role of b in the generalization ability of SVM for classification, optimization formulation of SVM without b is analyzed and the corresponding active set solution algorithm is proposed. By experiments on XOR classification problem, it can be concluded that SVM would fail to reach the optimum classification hyperplane due to the existence of constraint condition ∑1N yiαi= 0. Small to medium data sets, large data sets, high-dimension data sets and mutli-class classification data sets are employed in the simulations as well as the Gaussian positive definite kernel and polynomial positive definite kernel are used. The experimental results on 26 benchmark data sets show that the computational cost of SVM without b is over that of SVM and the generalization performance is over SVM. SVM without b is less sensitive to cost parameter, and this makes SVM without b reaches the optimal testing rate with less parameters pair values.