The penalty function method is one of the main approaches to transform the constrained optimization problems into unconstrained optimization problems. If the gradient of the objective function and constrained functions is not involved in the penalty function, the penalty function is simple. For the traditional exact penalty function, it can not be simple and smooth. For equality constrained optimization problems, a new class of simple penalty functions is constructed by adding a new variable to control the penalty terms. In this paper, the simple penalty functions have been proved smooth and exact. An algorithm based on the class of simple exact functions is proposed. Some numerical examples are given to show the efficiency of the algorithm.