This paper studied the back-stepping adaptive sliding mode control (SMC) attitude problem of quaternion aircraft model based on radial basis function (RBF) network approximation. Firstly, a sliding mode controller is designed based on the back-stepping method (BSM) for the nonlinear aircraft model. Secondly, a RBF network algorithm is designed to compensate for the unknown and uncertain parts of the aircraft system. RBF network has simple network structure and good generalisation ability, avoids lengthy and unnecessary calculations, realises adaptive approximation of unknown parts in the aircraft model, and through the adjustment of adaptive weights, the convergence and stability of the entire closed-loop system (CLS) are guaranteed. Finally, the anti-interference performance of the controller is verified by simulation of the actuator fault model. Our proposed method has all-right control performance indicated by the simulation results.