The paper is concerned with a trust region algorithm for solving the general nonlinear constrained optimization problem. The algorithm uses the \(L_\infty\) exact penalty function with a simple technique for updating the penalty parameters, which does not need to solve any auxiliary subproblems. Global convergence of the algorithm is proved, and also it is shown that for all large numbers of iterations the algorithm preserves the local superlinear convergence of the sequential quadratic programming method. Finally, some numerical results are given.