A fault tolerant controller design method based on predictive control is proposed for the hypersonic vehicle with elevator deflection stuck fault. The longitudinal model of hypersonic vehicle is transformed by using the input-to-output feedback linearization. The extended state observer is designed to estimate the higher derivatives of vehicle and altitude and the faulty functions online. The Talyor expansion is employed to obtain the predictive model, and the continuous predictive controller is constructed. Stability of the closed-loop control system and boundedness of observe errors are proved respectively. The illustrative simulations verify the effectiveness of the proposed method.