Automatic parking assist system is one of the key technologies in future automobiles. A car-like robot is difficult to control due to the nonholonomic constraints. In this paper, a path planning algorithm based on the slice projection techniqueoptimized particularly for car-parking is proposed. Collision-free region of a nonholonomic motion can be easily computed by using the slice projection technique. Sufficient collision-free, nonholonomic feasible paths can be directly obtained by computing reachable regions by using the slice projection technique for nonholonomic motions from the initial pose. The proposed planning scheme provide not a single solution, but a candidate solution set. Therefore, the parking path can be easily optimized with respect to performance criteria such as safety, maneuvering, and so on. The simulation results clearly show that the proposed scheme provides various practical solutions.