Abstract: To find smoothing functions with good performance,a plus function is transformed into an equivalent infinite series,thus deriving a class of polynomial smoothing functions.The important properties of them are discussed.It is shown that the approximation accuracy and smoothing rank of polynomial functions can be as high as required.The Newton-Armijo algorithm is used to solve the polynomial smooth support vector machine(PSSVM) finally.The experimental results show that as the smoothing rank of polynomial functions increases,the approximation accuracy and the classification performance of the PSSVM mode are correspondingly improved.