A time-matching system includes a first terminal device and a communications relay device relaying communications between the first terminal device and a second terminal device on a wireless communications network. The first terminal device receives a GPS-data from a GPS satellite, executes a first correction procedure on a satellite time-data of the GPS data to generate a first time-data, and transmits the first time-data to the communications relay device. The communications relay device receives the first time-data, executes an intermediate correction procedure on the first time-data to generate an intermediate time-data, and transmits the intermediate time-data to the second terminal device. The first correction procedure is based on a time delay in communications between the GPS satellite and the first terminal device. The intermediate correction procedure is based on a time delay in communications between the first terminal device and the communications relay device.