In this paper, the trajectory tracking problem is investigated for a nonholonomic wheeled mobile robot with parameter uncertainties and external disturbances. In this strategy, combining the kinematic model with the dynamic model, the actuator voltage is employed as the control input, and the uncertainties are approximated by a fuzzy logic system. An auxiliary velocity controller is integrated with an adaptive fuzzy integral terminal sliding mode controller, and a robust controller is employed to compensate for the lumped errors. It is proved that all the signals in the closed system are bounded and the auxiliary velocity tracking errors can converge to a small neighborhood of the origin in finite time. As a result, the tracking position errors converge asymptotically to zeros with faster response than other existing controllers. Simulation results demonstrate the effectiveness of the proposed strategy.