To further enhance the efficiency of AVP systems in crowded parking lots, the optimal trajectory planning problem for automated valet parking (AVP) is addressed in this paper. We propose a novel approach for AVP trajectory planning, which involves the transformation of a mixed-integer nonlinear programming (MINLP) problem of AVP trajectory planning into a two-stage nonlinear programming (NLP) problem. The first stage employs an enhanced Dijkstra algorithm that considers conflicts with other vehicles to find the global optimal trajectory during the drive phase to approach the assigned parking lot. In the second stage, the previously obtained trajectory is incorporated into a NLP to achieve the shortest parking time by optimizing the switching point between the driving and parking phase. Simulation results demonstrate that our proposed method can achieve the trajectory with optimized efficiency for AVP scenarios.