In a facsimile apparatus with a printer function, a facsimile receiver receives facsimile image data which is encoded according to a predetermined first facsimile coding method and is transmitted from a further facsimile apparatus of the other party, and a host interface interfaces the facsimile apparatus with an external computer and receives facsimile image data which is encoded according to a predetermined second facsimile coding method and is transmitted from the external computer. Further, a decoder decodes the received facsimile image data into image data, and a printer forms an image of the image data on a paper in response to the decoded image data. Furthermore, a MODEM is provided having a facsimile MODEM mode and a data communication MODEM mode which is switched over therebetween in response to command data transmitted from the external computer through a host interface. In the facsimile MODEM mode, the MODEM modulates a carrier signal according to facsimile image data and demodulates a modulated carrier signal according to facsimile image data received from the external computer. In the data communication MODEM mode, the MODEM modulates a carrier signal according to digital data received from the external computer and demodulates a modulated carrier signal according to digital data.