Support vector machine (SVM) is a new machine learning method developed from statistical learning theory. Since the objective function of the unconstrained SVM model is a non-smooth function, a lot of fast optimization algorithms can’t be used to find the solution. Firstly, to overcome the non-smooth property of this model, a new padé33 approximation smooth function is constructed by rational approximation method, and a new smooth support vector machine model (SSVM) is established based on the smooth function. Then, by analyzing the performance of the smooth function, we find that the smooth precision is significantly higher than existing smooth functions. Moreover, theoretical and rigorous mathematical analyses are given to prove the convergence of the new model. Finally, it is applied to the heart disease diagnosis. The results show that the Padé33-SSVM model has better classification capability than existing SSVMs.