We introduce in this talk an iterative algorithm for the differential linear complementarity problems consisting of two systems: the ODE system and the LCS system. Each iteration consists of two steps: by using a rough approximation of the state variable obtained from the previous iteration, we solve the LCS; then we solve the ODE system and update the state variable for preparing for the next iteration, by using the obtained constraint variable as a known source term. We prove that the algorithm converges superlinearly with arbitrarily chosen initial iterate. Numerical experiments indicate that this algorithm is superior to the widely used time-stepping method.