To address the challenges of abrupt curvature changes, high collision risks, and repeated adjustments in parallel parking within narrow urban passages, this study proposes a three-segment one-step path planning method integrating curve combination and numerical optimization to enhance vehicle’s steering performance and dynamic obstacle avoidance capabilities, and to improve the parking efficiency and safety. Firstly, based on the curvature characteristics of arcs and spiral curves, two types of curve combinations, namely CAC (Clothoid Curve-Arc-Clothoid Curve) and CC (Clothoid Curve-Clothoid Curve), are designed. Secondly, the parking process is reversed, and the CAC curve combination is used to design the path of the end section. Then, a constrained optimization model based on the CC curve combination is constructed to plan the path of the starting section, and the middle section path is designed by introducing the quintic polynomial curve. Finally, multi-condition simulation tests are carried out in the quasi-feasible area through Matlab. The results show that the proposed method can plan a collision-free and continuously curved feasible path in a narrow scene with a channel width of only 3 meters, without occupying wide channel. Comparative analysis reveals significant advantages of the proposed method over quintic polynomial curve and arc-clothoid curve-straight methods in terms of path smoothness, obstacle avoidance and space utilization efficiency. Model predictive control validation confirms that the vehicle adopting the proposed method is of precise path tracking performance with continuous front-wheel steering angle changes. The proposed three-segment one-step path planning method provides an efficient and safe solution to narrow-space parallel parking, and effectively improves the parking efficiency, thus alleviating road congestion caused by roadside parking operations and improving urban traffic efficiency.