Recent studies on automatic parking have actively adopted the technology developed for mobile robots. Among them, the path planning scheme plans a route for a vehicle to reach a target parking position while satisfying the kinematic constraints of the vehicle. However, previous methods require a large amount of computation and/or cannot be easily applied to different environmental conditions. Therefore, there is a need for a path planning scheme that is fast, efficient, and versatile. In this study, we use a multi-dimensional path grid map to solve the above problem. This multi-dimensional path grid map contains a route which has taken a vehicle's kinematic constraints into account; it can be used with the A* algorithm to plan an efficient path. The proposed method was verified using Prescan which is a simulation program based on MATLAB. It is shown that the proposed scheme can successfully be applied to both parallel and vertical parking in an efficient manner.