In the A* algorithm, path finding is slow and the generated path has redundant turning points. For these reasons, an A* algorithm with variable step sizes based on the steady-state steering model of vehicles is proposed. Firstly, the search step size of the A* algorithm is adjusted by setting sub-targets to reduce path finding time. Secondly, local replanning is performed according to the kinematic constraints on vehicle steering at the turning points of the global path. Thus, a smooth path of easy tracking is obtained. In addition, considering the actual width of an Unmanned Ground Vehicle (UGV), the improved algorithm also introduces an obstacle extension strategy to make the planned path meet the actual engineering application. Finally, the proposed algorithm is proved effective. A comparison between this algorithm and three path finding algorithms shows that the improved algorithm has obvious advantages over the other three algorithms, including shorter path finding time, smoother paths, and safe distance from obstacles being maintained.