This research aims to build a human following robot system based on a deep neural network algorithm in which a fuzzy controller controls the robot velocity and keeps the target person in the centre position of robot's view. Firstly, the system utilizes the deep neural network algorithm to detect a target person in the video sequence captured from a real sense D435 depth camera mounted on the mobile robot. Then, the system calculates the centre position of the target human and acquires the depth value of target human. Finally, these data are used as the inputs of a fuzzy controller to control the velocity and steering of the robot during tracking. Especially, the velocity of the robot which is normally limited as a constant in most existing human following robot systems is controlled by a fuzzy controller in this paper. The proposed system is verified through the experiments for a four-wheel steered mobile robot.