To solve the problem of high pilot cost in high-speed railway millimeter-wave wireless communication channel estimation, this study proposes a channel estimation scheme for millimeter-wave communication systems assisted by a reconfigurable intelligent surface (RIS). In this scheme, a Kalman filter (KF) is used to predict the channel, and the estimated channel state information (CSI) is obtained based on the correlation between adjacent time slots of the high-speed railway millimeter-wave channel. Then, an orthogonal matching pursuit (OMP) algorithm is used to recover the high-speed railway millimeter-wave sparse channel to obtain the optimal reflection matrix of the RIS. Finally, in the data transmission stage, the amplitude and phase of the RIS are adjusted according to the optimal reflection matrix to control the wireless transmission environment, thereby improving the transmission performance of the high-speed railway millimeter-wave wireless communication channel. Simulation results show that, compared with the traditional least squares (LS), minimum mean square error (MMSE), and OMP algorithms, the KF-OMP algorithm exhibits superior performance in time-varying channels.