The least l_2-norm solution for a possibley inconsistent system of nonlinear inequalities is studied in this paper. By introducing a new smoothing function, the problem is ap- proximated by a family of parameterized optimization prob- lems with twice continuously differentiable objective func- tions. Then a smoothing Levenberg-Marquardt method are applied to solve the parameterized optimization problems. The global convergence of the proposed method are established under some weak conditions. Numerical results show that the methods perform well.