Abstract: To solve the approximate linearly separable problem in pattern recognition,a new approximate linear Support Vector Machine(SVM) is presented.First,the two convex hulls from the training set of approximate linear classification are similarly squeezed into the linearly separable ones,and based on the two similarly squeezed linearly separable convex hulls,an optimal separating hyperplane is figured out by using the method of halving the nearest points and the maximal margin method.Then,the approximately linear SVM is obtained by solving the dual problem of maximal margin method.Finally,analysis is made from both theoretical and empirical aspects to compare the proposed new SVM,the known linear SVMs and the generalized method of halving the nearest points,and the advantages and rationality of the new SVM are demonstrated.