In this paper, a robust fault-tolerant controller is designed for flexible air-breathing hypersonic vehicle (HSV) with actuator fault and external disturbance. Firstly, the polytopic linear parameter variable (LPV) model of flexible HSV is established through Jacobian linearization and tensor product (TP) method. The integral terms of height error and velocity error are introduced to eliminate the steady state error, and the extended system is constructed. The actuator loss of effectiveness fault is separated from the control input and lumped into disturbance term together with the external disturbance. And the extended polytopic LPV faulty system is obtained. Secondly, the fault-tolerant controller is designed based on robust model predictive control (RMPC). The state feedback control law is obtained by solving the linear matrix inequality (LMI) optimization problem. Norm bounded theory is introduced to suppress the lumped disturbance term of the real system. The disturbed and undisturbed state are guaranteed to be in the same invariant set. Finally, numerical simulations have demonstrated the fault-tolerant performance of the developed controller.