There are provided a communication apparatus capable of performing voice communication via an IP network, and performing FAX communication using a deemed voice, and a method of controlling the same. At the time of reception of an incoming call, the apparatus determines whether an incoming voice communication call or digital data has been received. If it is determined that the incoming voice communication call has been received and there is an already connected voice communication section, the SLIC superimposes a tone of a notification of the incoming call during voice communication on a voice during voice communication. When the telephone instructs to switch to the incoming call, the apparatus establishes a new session for the incoming call, and controls the selector to connect the already connected voice communication session to the digital modem to send a holding tone.