Abstract: Differentiable and unconstrained quadratic programming can be constructed by improving a support vector machine (SVM) model using a smooth function, and thus a lot of fast optimization algorithms can be applied to solve the smooth SVM model. A new five-order spline function and a new seven-order spline function were constructed by a general three-moment method. These two spline functions are proved that their approximation accuracy is better than any other smooth functions, and the convergence accuracy of the spline function SVM model based on the five-order spline or seven-order spline is higher than any other smooth SVM models.