A prescribed-time adaptive control method is designed to solve the problem of stable trajectory tracking control of the hypersonic vehicle. The velocity and altitude tracking errors are guaranteed to converge to the desired area by introducing the barrier Lyapunov function while meeting the system's transient performance and steady-state accuracy requirements. By combining the adaptive control with the practically prescribed-time stability theory, the closed-loop system is stable at a prescribed time, and the convergence time can be predefined according to the actual needs. The introduced fixed-time filter is employed to solve the virtual derivative, which avoids the "term of explosion" problem in traditional backstepping control and improves the convergence speed. A rigorous theoretical proof is presented for the designed controller using the Lyapunov theory, which can ensure that the other state variables of the system tend to the steady-state value within a specified time. The simulation results show that the designed controller can make the velocity and altitude track the reference signals stably, and meet the time-varying performance constraints robustly.