This paper proposes a method of avoiding obstacles and tracking a moving object continuously and simultaneously by using new concepts of virtual tow point and fuzzy danger factor for differential wheeled mobile robots. Since differential wheeled mobile robot has smaller degree of freedom to control and are non-holonomic systems, there exist multiple solutions (trajectories) to control and reach a target position. The paper proposes 'fuzzy danger factor' for obstacles avoidance, 'virtual tow point' to solve non-holonomic object tracking control problem for unique solution and three kinds of fuzzy logic controller. The fuzzy logic controller is policy decision controller with fuzzy danger factor to decide which controller's result is more valuable when the mobile robot is tracking a moving object with obstacles to be avoided.