To provide an ATM network system capable of utilizing DNS without constructing an Ethernet(R) network even in the case of assembling a network just by an ATM switching network.

Since terminal equipment 1-1 does not recognize the VPI/VCI of a target WWW server 4-2, it generates a VPI/VCI conversion request based on the domain name of the WWW server 4-2 and sends it out to a VCI server 3. The VCI server 3 searches the one matched with the requested domain name based on the VPI/VCI conversion request. When the matched one is present, the VCI server 3 sends out a VPI/VCI converted result to the terminal equipment 1-1. When the VPI/VCI of the target WWW server 4-2 is converted by the VPI/VCI converted result, the terminal equipment 1-1 performs connection to the WWW server 4-2 based on the value of the VPI/VCI.