Abstract: This study proposes a Gaussian Radial Basis Adaptive Backstepping Control (GRBABC) system for a class of n-order nonlinear systems. In the neural backstepping controller, a Gaussian radial basis function is utilized to on-line estimate of the system dynamic function. The adaptation laws of the control system are derived in the sense of Lyapunov function, thus the system can be guaranteed to be asymptotically stable. The proposed GRBABC is applied to two nonlinear chaotic systems which have the different order to illustrate its effectiveness. Simulation results verify that the proposed GRBABC can achieve favorable tracking performance by incorporating of GRBFNN identification, adaptive backstepping control techniques.