In this paper, a trajectory tracking control for a nonholonomic mobile robot by the integration of a kinematic neural controller (KNC) and a torque neural controller (TNC) is proposed, where both the kinematic and dynamic models contain parametric and nonparametric uncertainties. The proposed neural controller (PNC) is constituted of the KNC and the TNC, and designed by use of a modeling technique of Gaussian radial basis function neural networks (RBFNNs). The KNC is applied to compensate the parametric uncertainties of the mobile robot kinematics. The TNC, based on the sliding mode theory, is constituted of a dynamic neural controller (DNC) and a robust neural compensator (RNC), and applied to compensate the mobile robot dynamics, significant uncertainties, bounded unknown disturbances, neural network modeling errors, influence of payload, and unknown kinematic parameters. To alleviate the problems met in practical implementation using classical sliding mode controllers and to eliminate the chattering phenomenon is used the RNC of the TNC, which is nonlinear and continuous, in lieu of the discontinuous part of the control signals present in classical forms. Also, the PNC neither requires the knowledge of the mobile robot kinematics and dynamics nor the time-consuming training process. Stability analysis and convergence of tracking errors to zero as well as the learning algorithms for weights are guaranteed with basis on Lyapunov method. Simulations results are provided to show the effectiveness of the proposed approach.