In recent years, transportation has been playing an important role in blooming logistics. Indeed, transportation accounts for more than 50% of the whole logistics cost. Express UAVs could effectively reduce the cost. Moreover, proper path-planning of UAV is also essential. Particularly, UAV should accurately avoid non-fly zones during flight. In this study, the obstacle avoidance path planning of UAVs is comprehensively discussed. With the improved A* algorithm and considering various obstacles, we propose a method that can find the optimal obstacle avoidance path between any two customer points. The simulation results prove the effectiveness of solving the obstacle avoidance path planning problem for express UAVs.