Path planning is the core technology to realize mobile robot navigation. The enhanced A* algorithm with a time elastic band method (TEB) is utilized to aim at the collision problem in a complex environment. A grid-based method transfers the complex environment to a simple grid-based map. The mobile robot's position is determined based on information from the given maps. Optimizing the search point strategy and removing redundant path points reduces the path length and computational scale. The approach yields a safe trajectory in the local path using a time elastic band. The collision cost function combined with the preview deviation angle tracking method ensures the minimum collision-free distance to obstacles and the shortest path. Furthermore, the third-degree B-spline curve will improve the performance of the mobile robot path at the steering angles. Simulated results illustrate the correctness of the proposed method.