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There are many on-orbit capture tasks for space robots. At present, most space robots capture methods are based on the trajectory planning of robot kinematics. This kind of method has poor control precision in space environment. The intelligence degree of robot capture task is very low. We built a simulation environment for robot space target capture task based on physics engine. A real-time online simulation training platform is established in the simulation environment. We design a robot deep reinforcement learning motion control model based on Actor-Critic algorithm. We optimize the reward function of the DRL model. The reward function shortens the training time and improves the score performance of the model. The experiment data show that the DRL model converges in 800 steps. The average score and standard deviation of the model indicate that the model has successful completed the capture task of space robot.