Reconfigurable intelligent surface (RIS) has received increasing attention due to its capability of extending cell coverage by reflecting signals toward receivers. This paper considers a RIS-assisted high-speed train (HST) communication system to improve the coverage probability. We derive the closed-form expression of coverage probability. Moreover, we analyze impacts of some key system parameters, including transmission power, signal-to-noise ratio threshold, and horizontal distance between base station and RIS. Simulation results verify the efficiency of RIS-assisted HST communications in terms of coverage probability.