For safe and feasible path-planning in real time of autonomous parking system, a parking path planning algorithm based on constrained reinforcement learning with a hybrid action space is proposed in this paper. Specifically, the proposed algorithm employs a hybrid action space reinforcement learning framework that integrates discrete actions with continuous parameters to achieve parameterized trajectory planning, thereby enhancing the executability of planned paths. On this basis, a constrained reinforcement learning algorithm within the hybrid action space is designed to optimize safe policy execution, ensuring the safety of parking paths. Moreover, a curriculum learning mechanism is introduced during model training to guide exploration progressively, improving training stability and convergence speed. Finally, extensive comparative and ablation experiments are conducted on both perpendicular and parallel parking scenarios. The experimental results show that the proposed parking path planning algorithm outperforms existing state-of-the-art methods in terms of success rate, safety, and real-time performance, exhibiting superior overall effectiveness.