In recent years, drones have developed rapidly in the field of logistics and transportation. An important reason is that drones could cope with various complex traffic environments such as urban traffic congestion and poor road conditions in remote rural areas. Path planning is a key part of their practical application process. This study designs an adaptive large neighborhood search algorithm for it. The algorithm improves the traditional neighborhood search by introducing an adaptive mechanism, so that it has the potential to find better solutions. Simulation experiments on some classic datasets show that the proposed algorithm has strong robustness and stability. In addition, comparative experiments with other meta-heuristic algorithms verify that the proposed algorithm can effectively reduce the cost of logistics distribution with a drone.