Heuristic dynamic programming (HDP) design for autonomous mobile robot was put forward to solve the goal seeking with obstacle avoidance problem. A method of sensor detecting was proposed, and the method for system normalizing the sensors’ inputs information was discussed. The input/output signal and reinforcement signal were defined, and a self learning strategy for robot seeking the goal with obstacle avoidance was proposed. A continuous reinforcement signal to improve the systems preferential decision between goal seeking and obstacle avoidance was designed. To verify the learning ability of our algorithm, three different simulation experiments were designed: same goal with different initial points and directions, same initial states with different goals, moving goal. The simulation results show that the HDP approach presents an effective learning ability for autonomous mobile robot on goal seeking with obstacle avoidance problem.