The invention provides a pump for liquid chromatography excellent in feeding liquid stably at an extremely low flow rate with high accuracy and in discharging bubbles at startup.At startup, a first plunger feeds solvent at a large flow rate to discharge bubbles in a pump and to fill the solvent into the pump in a short time and in a normal operation, the first plunger is stopped and the second plunger is pushed into a second pressure chamber at a low speed to feed the solvent at a low flow rate. When the second plunger reaches full stroke, the second plunger is pulled back at a high speed and at the same time the first plunger is pushed into a first pressure chamber in synchronization with the pullback of the second plunger to control the flow rate passing a discharge passage to a constant value at all times by a controller. Further, while the second plunger feeds the solvent, the first plunger is slightly pushed into the first pressure chamber to keep pressure in the first pressure chamber at pressure equal to or less than pressure in the second pressure chamber.