Abstract: A network accessing system of a computer includes a wire communicating unit for wire access to a network; a wireless communicating unit for wireless access to the network; a sensing unit for sensing a connection of the wire communicating unit to the network; and a controlling unit for disabling the wireless communicating unit when it is sensed that the wire communicating unit is connected to the network, as a result of sensing by the sensing unit. With this configuration, the present invention provides a network accessing system of a computer system equipped with both devices available for connection to the wire network and the wireless network, thereby saving power consumption by a networking device when the other device is connected to a network, and a method of controlling the same.