An air-conditioner communication system includes an air conditioner, a wireless LAN adapter attached to the air conditioner and having a function as a network communication unit of the air conditioner, a router configuring a local area network with the wireless LAN adapter, a server communicable with the router via a telecommunication line, and a terminal device communicable with the wireless LAN adapter and having a display, in which the wireless LAN adapter has a function of acquiring connection information as to whether the wireless LAN adapter is communicable with the router and providing the terminal device with the connection information.