A method for filling a liquid-discharge-head cartridge with liquid includes a first step in which a suction operation is performed at a first suction pressure while a suction member is moved along the discharge port row in the discharge-port surface at a first moving speed to suck the liquid in the liquid container to fill the discharge ports, and a second step in which a suction operation is performed at a second suction pressure, which is lower than the first suction pressure, while the suction member is moved along the discharge port row in the discharge-port surface at a second moving speed, which is lower than the first moving speed to remove bubbles in the flow path.