Abstract: Sigmoid function is used as the smoothing function in Smooth Twin Support Vector Regression (STSVR). However,the approximation accuracy of Sigmoid function is low.In order to overcome this problem,in this paper, a new smooth twin support vector regression, term as Polynomial Smooth Twin Support Vector Regression (PSTSVR),is proposed.In PSTSVR,plus function is transformed to an infinite polynomial series.Thus a family of smoothing functions is derived. Polynomial function is used to approximate the non-differential term of twin support vector regression.Then Newton-Armijo algorithm is used to solve the corresponding model.We have proved that PSTSVR is not only convergent,but also can meet the arbitrary order smooth performance.Meanwhile, the experimental results on several artificial and benchmark datasets show that PSTSVR has better regression performance than STSVR.