Automatic vehicle parallel parking design and its related concerns about safety improvement remain some of the heated problems for automatic land vehicular control. This paper presents the calculation process of a parallel parking car's path planning and the algorithm development for its motion design based on a fifth-degree polynomial curve. In addition to the proposed algorithm for automatic vehicle parking, the minimum horizontal distance allowed for parking between a car and a parking spot is also investigated. The preliminary results show that the fifth degree polynomial path planning and the algorithm are well applied to the automatic parallel parking problem.