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A hybrid control algorithm is proposed based on a backstepping kinematic control and a PID sliding mode dynamic control with an adaptive neural network adjust gain of sliding mode control for trajectory tracking control of nonholonomic mobile robot. Parameters and non-parameter uncertainties of mobile robot can be solved by using the robust control which takes advantages of stability and robustness in PID sliding mode control. The gain of sliding mode control is adjusted by using the RBFNN control with adaptive tuning algorithm, which enhances the adaptability for random uncertainty and eliminates input chattering of the sliding mode control. The stability and convergence of the control system are proved by using the Lyapunov method. The simulation results demonstrate that the controller has smooth control input, and the tracking errors of nonholonomic mobile robot are eliminated.