In an Internet telephone connection method, a communication bandwidth is managed by using a bandwidth controller, gateway devices and voice relay routers to monitor communication quality under bandwidth reservation. A communication path under bandwidth reservation is preferentially selected by using gate keepers and the voice relay routers, and the connection of the Internet telephone is performed. A problematic device is prohibited from being selected as a connection-destination device at the time of a call setup and the problem restoration is monitored by using the gate keepers and the gateway devices. Further, a device having invalid attribute information is prohibited from being selected as a connection-destination device at the time of call-setup, and the restoration of the attribute information is notified to the overall network. Accordingly, the reservation of the communication bandwidth can be performed under the control of the overall network, fixed communication quality can be maintained and reliability can be enhanced.