An object of the present invention is to provide a communication system which can efficiently transfer data having a comparatively large capacity from a network interface through a radio interface. A mobile telephone is allowed to access a contents server from a base station through a mobile communication network and the Internet. Although the sum of electric power which the base station simultaneously transmits to all of the mobile telephones has an upper limit, the transfer rate to any mobile telephone that is transmitting or receiving large data are changed to a higher level, within a range of a margin. The electric power to the mobile telephone may be checked, and the data transfer rate may be increased when the checked electric power is small.