Aiming at the uncertainties of the mobile robot trajectory tracking processes, an H∞ sliding mode controller was designed by utilizing the ideas of Backstepping and Lyapunov method. The switch gain of the sliding mode controller was optimized by adaptive fuzzy control to eliminate the chattering in sliding mode control. Finally, three trajectory tracking simulation experiments consisting of straight, circular and sinusoidal trajectories were carried out to verify the global asymptotic stability and anti-interference performance of the system, respectively. And the results demonstrate the effectiveness of the control strategy.