The automatic parking system can replace people to complete the parking task and reduce the burden of driving. The size of the parking space affects the number of parking operations and the time for parking planning to be completed. Parking planning in narrow space is a challenging problem, especially in crowded urban environments. This paper presents a parking path planning method in a narrow vertical parking space. First, the parking path planning method can be used in narrow corridor spaces and narrow spots. According to the size of the corridor space and the parking space obtained by the environment perception, this method can determine the number of parking maneuvers and the start parking position. Second, to allow the vehicle to generate a parking path at any position to reach the parking starting point, the system generates a target line set that considers control error factors. It will also select the optimal target line based on the current position. Third, the vehicle cannot complete the parking while traveling along the original parking path when the factual error is greater than the reserved error. Therefore, a re-planning method based on geometric planning is proposed to improve the robustness of the system. Finally, through the establishment of longitudinal and lateral driver models, the effectiveness of the path planning method is verified, and compared with other path planning methods, it proves that the method proposed in this paper performs well in the number of maneuvers and planning time in a small space.