An ink-jet printer, including an ink-jet recording head having an ink inflow passage including an ink inlet, and an air-discharge passage which allows the ink inflow passage to communicate with an atmosphere; an air-discharge valve which selectively opens and closes the air-discharge passage; an ink tank which stores the ink and which has an ink outlet and an air inlet; a connector having an ink supply passage which communicates, at one end thereof, with the ink outlet of the ink tank and communicates, at an other end thereof, with the ink inlet of the recording head; an air supplying device which supplies the air to the ink tank via the air inlet thereof; an obtaining portion which obtains one of an elapsed time, t, from a reference time, and a volume, V, of an air present in the ink supply passage and the ink inflow passage at the elapsed time t, based on an other of the elapsed time t and the air volume V, and a following relationship: V=a·ebt, where a and b are coefficients and e is a base of a natural logarithm; and a control portion which controls, based on the obtained one of the elapsed time t and the air volume V, an operation of the air supplying device and / or the air-discharge valve, so that the volume V of the air at the elapsed time t is discharged through the air-discharge passage opened by the air-discharge valve.