To ensure the safe and reliable operation of high -speed trains, this paper develops a new adaptive control scheme for the braking system of high-speed trains with unknown disturbances and input time delays， which realizes the asymptotic tracking of given speed curve. By analyzing the principle and dynamic characteristics of braking systems, a state space model of high-speed trains with disturbances and input time delays is established. A state feedback control law is designed based on state prediction and the capacity of model reference adaptive control to deal with system uncertainties and disturbances, thus realzing the asymptotic tracking of given speed curve in presence of unknown disturbances and input time delays. The data in Jinan-Qingdao section of CRH380AL type of high-speed trains are used for simulation study. Simulation results show the desired stability, tracking performance, and robustness in dealing with unknown parameters and bounded disturbance.