In this paper, a trajectory tracking control for a nonholonomic mobile robot subjected to kinematic disturbances is proposed. A variable structure controller based on the sliding mode theory is designed, and applied to compensate these disturbances. To minimize the problems found in practical implementations of the classical variable structure controllers, and eliminate the chattering phenomenon, is used a neural compensator, which is nonlinear and continuous, in lieu of the discontinuous portion of the control signals present in classical forms. This proposed neural compensator is designed by the Gaussian radial basis function neural networks modeling technique and it does not require the time-consuming training process. Stability analysis is guaranteed based on the Lyapunov method. Simulation results are provided to show the effectiveness of the proposed approach.