A smooth time-varying controller is proposed to simultaneously address the stabilization and tracking problems of nonholonomic mobile robots for most admissible reference trajectories without switching. The controller is developed with the aid of a delicately designed time-varying signal and Lyapunov method. Computational simplification and asymptotic convergence of regulation or tracking errors are achieved by the proposed controller. Our approach provides an interesting way to unify the existing results on point stabilization and trajectory tracking of mobile robots. The simulation and experimental results on a wheeled mobile robot are presented to demonstrate the effectiveness of the proposed controller.