In the paper, a new trust region algorithm is given for nonlinear inequality constrained optimization problems. Motivated by a dual problem introduced by Han and Mangasarian [Han, S. P., Mangasarian, O. L. (1983). A dual differentiable exact penalty function. Math. Programming 25:293-306], which is a nonnegatively constrained maximization problem, we construct a trust region algorithm for solving the dual problem. At each iteration, we only need to minimize a quadratic subproblem with simple bound constraints. Under the condition that the iterate sequence generated by the algorithm is contained in some bounded closed set, any accumulation point of the sequence is a Karush- Kuhn-Tucker point of the original problem. [ABSTRACT FROM AUTHOR]