An Internet facsimile gateway device that exchanges image information between a data terminal device and a facsimile device through a telecommunication network and the Internet by taking the steps of transmitting the image information included in an electronic mail message to the facsimile device when the Internet facsimile gateway device receives the electronic mail message requesting image-information transmission to the facsimile device, creating a delivery-confirmation mail message notifying a result of the image-information transmission after the image-information transmission by the Internet facsimile gateway device is completed if the electronic mail message requests the Internet facsimile gateway device to transmit the delivery-confirmation mail message to an original address of the electronic mail message, and transmitting the delivery-confirmation mail message to the original address of the electronic mail message.