In this paper,we propose an algorithm for solving inequality constrained mini-max optimization problem.In this algorithm,an active set strategy is used together with multiplier method to convert the inequality constrained mini-max optimization problem into unconstrained optimization problem.A trust-region method is a well-accepted technique in constrained optimization to assure global convergence and is more robust when they deal with rounding errors.One of the advantages of trust-region method is that it does not require the objective function of the model to be convex.A global convergence analysis for the proposed algorithm is presented under some conditions.To show the efficiency of the algorithm numerical results for a number of test problems are reported.