An internet facsimile communication system capable, in the internet facsimile based on the Recommendation T.38, of receiving an incoming call for a facsimile communication regardless of the setting of receiving mode in the facsimile apparatus thereby avoiding a drawback that a person responds to a facsimile communication.The internet facsimile communication system comprises an adaptor for connection with an IP network and a G3 facsimile apparatus, in which the adaptor changes the format of a call signal for calling the G3 facsimile apparatus, between an incoming call for a facsimile communication and other incoming call, thereby informing the G3 facsimile apparatus of an incoming call for the facsimile communication.