Abstract: Both a connection server and a relay connection server are installed in an IP transfer network; a function similar to a line connection control of a subscriber exchanger is applied to a connection server; a function similar to a line connection control of a relay exchanger is applied to the relay connection server; and a terminal-to-terminal communication connection control method with using the IP transfer network is realized in such a manner that a telephone set and a terminal such as an IP terminal and a video terminal transmit/receive an initial address message, an address completion message, a call pass message, a response message, a release message and a release completion message, which can be made in a 1-to-1 correspondence relationship with line connection control messages of the common line signal system.