Abstract: Smoothing functions play an important role in Support Vector Machines（SVM），and to find out a good smoothing function is the key to research SVM.The paper derives and proves the performance of a 6th-order smoothing function using the differentiation method，and analyzes its approaching performance using dichotomy.The results show that the approximation accuracy of this 6th-order smoothing functions is better than that of the previously used smoothing functions.So it also provides a new smoothing function for further studying of SVM.