The complete coverage path planning algorithm based on A* algorithms for the cleaning robot in known environment is proposed in this paper, which uses A* algorithm as heuristic in the U-turn search algorithm. The idea of this algorithm is the cleaning robot clean the cleaning area from the point of origin by using U-turn algorithm, then planning of the shortest path from cleaning robot to not clean area by using A* algorithm when the robot into the dead nodes, and then the cleaning robot for sweeping along this path to not cleaning area by using U-turn search algorithm until this environment area is all covered. The simulation results show that this algorithm proposed of this paper is high coverage rate and low repetition rate.