The turning constraint and start/goal angle constraint are often needed to be considered in the actual robot path planning problem, and the A* algorithm based on direction constraints is proposed in this paper. Paths in the same path point are distinguished by their different directions in the algorithm, and the direction constraints of paths are met by the directional extension mechanism, while the node merging strategy and the inconsistent list are adopted to reduce the algorithm complexity. Theoretical analysis and experimental results on the typical map set show that the propoved algorithm can always guarantee to give the shortest path which conforms to the turning constraint and start/goal angle constraint. Compared with the existing algorithms, the proposed algorithm can improve the ability of solving path planning problem with direction constraints effectively.