Due to disturbances and noise, mobile robots are unavoidably away from a desired path. Thus how to control a mobile robot to track the path is a fundamentally important issue in robotics. In this thesis, a novel tracking control approach is developed for a car-like robot, which is based on the backstepping techniques and a neural dynamics model. The proposed control algorithm can generate smooth and reasonable velocity commands. It resolves the problem of the speed thrust jump caused by most previous tracking controllers, which is not true in the real world. In addition, unlike some existing path trackers, the proposed tracking controller can deal with arbitrarily large tracking errors. A novel tracking control algorithm for a discrete trajectory is proposed as well. The stability of the control systems are analysed and proved using a Lyapunov stability theory. Simulation results demonstrate the efficiency of the proposed tracking control algorithms. Some comparisons are conducted to illustrate that the proposed control algorithms excel the previous backstepping-based approaches. A path information based path-tracking model for point robots is also proposed. The integrated system of the path planner and the path tracker is also simulated in this thesis.