Many kinds of practical problems can be formulated as nonlin-ear complementarity problems. In this paper, an inexact alternating direction method of multipliers for the solution of a kind of nonlinear complementar-ity problems is proposed. The convergence analysis of the method is given. Numerical results confirm the theoretical analysis, and show that the proposed method can be more efficient and faster than the modulus-based Jacobi, Gauss-Seidel and Successive Overrelaxation method when the dimension of the problem being solved is large.