Hypersonic vehicle is susceptible to external disturbances during maneuvering. If traditional state feedback control methods are used, the closed-loop control system can easily cause oscillations and fail to meet the precision requirements for the tracking of maneuvering flight instructions. If traditional sliding mode control methods are used, the problem of singular value will emerge in the system and the calculation process is more complicated, thus the control system is difficult to implement. In view of the above problems and considering the actual requirements of high-speed maneuvering flight control, this paper proposes a designed method of the linear parameter varying (LPV) controller based on a finite-time time-varying sliding mode and applies it to hypersonic vehicle control. First, the system was kept stable by traditional state feedback control methods without taking the external disturbances into account. Then, in the presence of perturbations, a finite-time time-varying sliding mode control law was developed by selecting a special sliding function. In order to reduce the chattering phenomenon of the system, a saturation function was introduced to replace the signed function in the control law. Theoretical derivation proved that all the signals in the closed-loop system are bounded, and the tracking error can be controlled to a small neighborhood around the origin in a predetermined time. Simulation results show that the states of the hypersonic vehicle could stably track the reference signal within a limited time, and the oscillation phenomenon of the closed-loop system was effectively suppressed. These properties verified the effectiveness of the controller presented in this paper.