To provide a wireless LAN system, a sleep mode is set for reducing consumed power and, when an arrival of the own address side is present, wake-up is caused to reliably receive the arrival. Specifically, a plurality of hosts 20 such as PC interconnected with an access point 30 via a wireless LAN each include a wireless LAN device 21, the power supply thereof being turned on and off in synchronism to a beacon signal 32 sent out in a predetermined constant cycle from the access point 30 for checking whether any arrival of data addressed to the own host 20 is present. When any arrival 33 of data is present the host 20 starts an application for reception of the arrived data.