We study on acquisition of behavior to follow a specific person, while keeping a certain distance by using reinforcement learning. In the previous paper, we have already confirmed that the robot can acquires the behavior by using an angle of a pull string which connects the person and the robot as the reward of the learning. In this paper, to keep a certain distance, the stop action is added to the robot. And, the distance between the person and the robot is used for the reward in the learning phase. We confirm the effectiveness of the proposed method through an experiment.