In this paper, we propose an Openspace Collision-freE trAjectory plaNner (OCEAN) for autonomous parking. OCEAN is an optimization-based trajectory planner accelerated by Alternating Direction Method of Multiplier (ADMM) with enhanced computational efficiency and robustness, and is suitable for all scenes with few dynamic obstacles. Starting from a hierarchical optimization-based collision avoidance framework, the trajectory planning problem is first warm-started by a collision-free Hybrid A* trajectory, then the collision avoidance trajectory planning problem is reformulated as a smooth and convex dual form, and solved by ADMM in parallel. The optimization variables are carefully split into several groups so that ADMM sub-problems are formulated as Quadratic Programming (QP), Sequential Quadratic Programming (SQP),and Second Order Cone Programming (SOCP) problems that can be efficiently and robustly solved. We validate our method both in hundreds of simulation scenarios and hundreds of hours of public parking areas. The results show that the proposed method has better system performance compared with other benchmarks.