Path planning is a fundamental problem in the aspect of autonomous driving. A-star (A*) algorithm is a heuristic algorithm for path planning. However, there are two problems need to be solved in the traditional A-star algorithm: firstly, the tracking error caused by vehicle speed and vehicle size are not considered in path planning; secondly, the kinematics constraints of the vehicle itself and the smoothness of the path in the actual driving process are not considered. Therefore, this paper proposes an improved A-star algorithm to address the above deficiencies. By designing the collision cost heuristic function based on the position of obstacles, the vehicle contour and speed are considered and the vehicle safety is improved by setting a safe space around the vehicle, and establishing a steering cost heuristic function based on the control of heading angle difference, the vehicle dynamics constraints are satisfied, so as to improve the feasibility of path planning. The experimental results show that the improved A-star algorithm can avoid vehicle contours collision at different speeds and output a smoother path, and effectively generate higher quality path.