In this paper, we consider the solution of linear weighted complementarity problem (denoted by LWCP). Firstly, we introduce a new class of weighted complementary functions and show that its continuously differentiable. On this basis, the LWCP is reconstructed as a smooth system of equations, and then solved by the Levenberg-Marquardt method. The convergence of the algorithm is proved theoretically and numerical experiments are carried out. The comparative experiments show that the algorithm has some advantages in computing time and iteration times.