In the logistics robot transportation process, path planning is the core link, facing challenges such as insufficiently smooth paths and low algorithm search efficiency. The A* algorithm, as a widely used global path planning method, has problems such as ineffective path smoothing when applied to logistics robots. To this end, the traditional A* algorithm has been improved by dynamically weighting the heuristic function and using the Floyd algorithm to remove redundant points in the path, while introducing a safe distance mechanism to prevent collisions. In addition, the path has been smoothed and optimized to better adapt to the actual movement needs of logistics robots. The MATLAB simulation results show that the improved A* algorithm reduces the average number of turning points by 58.5%, shortens the path length by 3.19%, and reduces the number of traversal points by 59.9% compared to traditional algorithms. Further combining with DWA algorithm for local path planning, obstacle avoidance function has been achieved. The effectiveness of the fusion algorithm has been verified through simulation and real vehicle experiments.