In this paper, we propose the parameter-Newton (PN) method to solve the second-order linear complementarity problem (SOCLCP). The key idea of PN method is that we transfer the SOCLCP into a system of nonlinear equations by bringing in a parameter. Then we solve the system of nonlinear equations by Newton method. At last, we prove that the PN method has quadratic convergence. Compared with the bisection-Newton (BN) method, the PN method has less CPU time and higher accuracy in numerical tests.