<p>In this paper, we introduce a new class of CHKS smoothing functions and show that the new smoothing functions possess a system of desirable properties. Based on the new smoothing functions, we obtain a smoothing homotopy method for solving the second-order cone complementarity problem. Under appropriate assumptions, we prove that the proposed method determines a smoothing interior path from a given interior point to an interior point where the necessary conditions are satisfied. The numerical tracing of this path gives a globally convergent algorithm for the SOCCP. Finally, some numerical results are reported, showing that the considered algorithm is applicable and efficient.</p>