The exact penalty function commonly used in the solution of nonlinear programming problems has a significant disadvantage of non-smoothness, which hinders the use of fast and effective minimization algorithms, and may cause some numerical instability. Therefore, this paper consider a method to smoothly approximate exact penalty function A, and gives the error estimation among smoothing penalty problem, the problem of nonsmooth penalty and the optimal objective function value of the original problem. On the basis of the given smoothing function, an algorithm for calculating the approximate optimal solution of the problem is proposed and the convergence of the algorithm is given.