An ink-jet printing apparatus can maintain a liquid level height in an ink storing portion in an air buffering vessel at a predetermined height and can simplify an associated mechanism for connection between a scanning carriage and a stationary ink tank while a low cost single tube is employed. An air buffering vessel of the ink-jet printing apparatus has one ink supply opening from the ink storage tank and at least two suction and discharge openings located at mutually different height in a vertical direction. Upper opening of the at least two suction and discharge openings serves for air suction and discharge. Lower opening serves for ink supply and discharge, and is communicated with a connection opening of the printing head.