The human-following behavior design for mobile robots is considered in this paper. In particular, the issue should be addressed from the perspective of human-robot interaction since humans are aware of the following actions. This makes the problem quite different from human tracking where recognition and location accuracy are the main concerns. An anticipative humanfollowing behavior is proposed by incorporating the human model. The human model is constructed using relevant scientific studies about human walk and social interaction, allowing the robot to predict the human trajectory and to take preemptive action. To realize the idea, it is necessary to have a robust sensing system that is capable of tracking the human location persistently. In this paper, we also propose a sensing system based on a novel 3-D meanshift algorithm on RGBD camera. The system performance is assessed through experimental evaluation of three specific humanfollowing scenarios: following from behind, following on the side, and following in front. Each of these scenarios has its particularities and applications, thus providing insight about the effectiveness and usability of anticipative behavior.