This paper proposes a novel fuzzy control scheme for flexible air-breathing hypersonic vehicle (FAHV) non-affine models with amplitude and rate constraints. First, the non-affine dynamics of the FAHV is decomposed into velocity subsystem and altitude subsystem, then the non-affine models of each subsystem are converted into equivalent pure feedback forms, and the fuzzy approximator is used to estimate the total uncertainties of each subsystem. Since the input of control system can be limited by the actual actuator, a new error compensation auxiliary system is proposed to solve the amplitude and rate constraints of the actuator, and a fuzzy controller with auxiliary systems is designed. The stability of the closed-loop system is proved by the Lyapunov method. Through simulation verification, the effective performance of the control system has been proved. INDEX TERMS Fuzzy approximator, flexible air-breathing hypersonic vehicle (FAHV), non-affine dynamics, error compensation auxiliary system, amplitude and rate constraints.