In order to plan a safe and effective UAV trajectory for quay crane inspection, this paper proposes a UAV trajectory planning method using Light Detection and Ranging (LiDAR) scanner. Firstly, viewpoints of UAV inspection are selected according to LiDAR and detected surface of quay crane. Secondly, vector jump point search algorithm (VJPS) is proposed to generate a collision-free path. Finally, by applying corridor constraints and deviation function, four inspection trajectories are simulated according to the dynamic characteristics of UAV. The simulation results show that the proposed path planning method can decrease 5.79% search time and 15.52% total path length, the proposed trajectory optimization method can generate a trajectory close to the planned path, which reduces the deviation distance between the planned path and actual trajectory. Overall, it appears that when tracking the trajectory generated by the above method, a LiDAR-equipped UAV can accomplish inspection tasks more effectively and safely in the quay crane environment.