The Weighted Complementarity Problem (WCP) significantly extends the general complementarity problem and can be used for modeling a larger class of problems from science and engineering. In this talk, we will introduce a smoothing Newton algorithm by using a one-parametric class of smoothing functions. We will discuss the global convergence and local superlinear or quadratic convergence of this algorithm without nonsingularity assumption on the Jacobian. Some numerical results of this algorithm will be also discussed.