A global asymptotically stable feedback tracking controller is proposed for the speed saturation constraint commonly existed in non-complete wheeled mobile robots. Firstly, a new virtual control quantity was constructed based on state feedback, and the kinematics control law was constructed by using Lyapunov’s theorem. Then the bounded velocity control was realized by using the mobile robot’s velocity saturation constraint and restricted control parameters. Finally, the corresponding stability analysis was carried out. Compared in simulation with the controller without considering the speed saturation constraint, the results show that the actual trajectory is smoother and closer to its reference trajectory, which improves the accuracy of trajectory tracking.