This liquid feeding system has the first and second pumps each of which is provided with a plunger. Liquid sucked through each of the pump suction ports is discharged out of the discharging port through the first pump and/or second pump. Under the starting operation mode, the second pump is stopped and only the first pump is operated. When the discharging pressure at the discharging port reaches up to a predetermined value, the starting operation mode is changed over to the normal operation mode. Under the normal operation mode, the first pump is stopped and only the second pump is operated.