Data produced from a transmission source facsimile are received by a simulated communication circuit network, and thus received data are compressed and temporarily stored into a memory. After the data have been compressed, the data stored in the memory are read out and transmitted to an other party's facsimile via an external communication circuit network. Since the data transmitted to the other party's facsimile via the external communication circuit network are compressed data, a time required for transmission can be relatively shortened. Accordingly, a rapid data transmission can be achieved without the facsimile being replaced by a rapid type facsimile which is expensive. Further, various additional functions of a facsimile can be directly enjoyed from those intrinsically owned by the transmission source facsimile. In addition, such arrangements may be made that a time presumably required for communication via the simulated communication circuit network is measured as a presumed time of communication in the normal transmission mode, while an actual time of communication in which a rapid transmission has been done by means of highly compressed data is measured, and that both the presumed communication time and the actual communication time are notified to the user so that the user can realize having saved the communication cost by means of the transmission involving data compression.