Strong coupling between the elastic body and the propulsion system in a hypersonic vehicle is caused by its integrated pneumatic layout and strong nonlinearity uncertainty, and obvious time-varying characteristics of aerodynamics, when the vehicle spans a large airspace and is flying at high speed. To eliminate the influence of this coupling, we propose a backstepping sliding mode control scheme based on a recurrent cerebellar model articulation controller (RCMAC). The input-output feedback linearization approach is used to resolve coupling between multiple variables. Firstly, we established the nonlinear mathematical longitudinal model of a hypersonic vehicle. Secondly, the sliding mode variable structure controller was designed to do away with the uncertainty of mismatch. Finally, the RCMAC-based backstepping sliding mode controller was designed. The controller makes up for the shortcoming of robustness of the hypersonic vehicle by its control structure and ability of nonlinear approximation and self-learning. The results of the simulation experiment indicate that the longitudinal altitude and velocity control precisions of a hypersonic vehicle can reach 0.5 m and 0.1 m/s, respectively and can therefore satisfy the system requirements of global stability, good dynamic responses, and robustness.