In this article, we propose an adaptive backstepping control scheme using fuzzy neural networks (FNNs), ABCFNN, for a class of nonlinear non-affine systems in non-triangular form. The nonlinear non-affine system contains the uncertainty, external disturbance or parameters variations. Two kinds of FNN systems are used to estimate the unknown system functions. According to the FNN estimations, the adaptive backstepping control (ABCFNN) signal can be generated by backstepping design procedure such that the system output follows the desired trajectory. To ensure robustness and performance, a proportional-integral- surface function and robust controller are designed to improve the control performance. Based on the Lyapunov stability theory, the stability of a closed-loop system is guaranteed and the adaptive laws of the FNN parameters are obtained. This approach is also valid for nonlinear affine system with uncertainty or disturbance. The uncertainty and disturbance terms are estimated by FNNs and treated by the ABCFNN scheme. Finally, the effectiveness of the proposed ABCFNN is demonstrated through the simulation of controlling a nonlinear non-affine system and the continuously stirred tank reactor plant to demonstrate the performances of our approach.