This paper investigates the attitude-orbit integrated modeling and robust control of flexible spacecraft with input saturation. First, the dual-number method is employed to describe the dynamic model of the spacecraft with the flexible appendage. Then, a fast terminal sliding mode control law is designed to stabilize the attitude-orbit control system of the spacecraft. In addition, considering the input saturation, a time-varying siding surface based terminal sliding mode control law is further proposed to solve the design problem. Under the designed control laws, the state trajectories of the attitude-orbit coupled control systems can achieve to be finite-time stable, and the reachability of the proposed sliding surface can be ensured at the same time. Finally, through numerical simulations and comparison with the conventional methods, the superiority of the proposed control strategies in convergence speed and convergence accuracy is verified, and the feasibility of engineering application is verified.