As one of the core issues of the mobile robot motion control, trajectory tracking has received extensive attention. At present, the solution of the problem only takes kinematic or dynamic model into account separately, so that the presented strategy is difficult to realize satisfactory tracking quality in practical application. Considering the unknown parameters of two models, this paper presents an adaptive controller for solving the trajectory tracking problem of a mobile robot. Firstly, an adaptive kinematic controller utilized to generate the command of velocity is designed based on Backstepping method. Then, in order to make the real velocity of mobile robot reach the desired velocity asymptotically, a dynamic adaptive controller is proposed adopting reference model and Lyapunov stability theory. Finally, through simulating typical trajectories including circular trajectory, fold line and parabola trajectory in normal and perturbed cases, the results illustrate that the control scheme can solve the tracking problem effectively. The proposed control law, which can tune the kinematic and dynamic model parameters online and overcome external disturbances, provides a novel method for improving trajectory tracking performance of the mobile robot. As one of the core issues of the mobile robot motion control, trajectory has been acquired extensive attention. At present, the solution of the problem only takes kinematic or dynamic model into account separately, so that the presented strategy is difficult to realize satisfactory tracking quality in practical application. This paper presents an adaptive controller for solving the trajectory tracking problem of a mobile robot. Firstly, an adaptive kinematic controller utilized to generate the command of velocity is designed based on Backstepping method. Then , in order to make the real velocity of mobile robot reach the desired velocity asymptotically, a dynamic adaptive controller is proposed to apply reference model and Lyapunov stability theory. Finally, through simulating typical trajectories including circular trajectory, fold line and parabola trajectory in normal and perturbed cases, the results illustrate that the control sc he can solve the tracking problem effectively. The proposed control law, which can tune the kinematic and dynamic model parameters online and overcome external disturbances, provides a novel method for improving trajectory tracking performance of the mobile robot.