In an ink-jet head device, a main tank, a sub tank and an ink-jet head are mounted in this order in a carriage, with the main tank placed at the top. The main tank, sub tank and ink-jet head are connected to one another by a three-way ink conduit. At a junction of the ink conduit is disposed a three-way switching valve, which selectively switch a path connecting the sub tank to the main tank and a path connecting the sub tank to the ink-jet head, without causing the ink-jet head and the main tank to communicate with each other. As a result, an ink-jet head device and an ink-supplying method are realized, in which the ink-jet head can maintain suitable negative pressure and in which consumption of ink is reduced.