Provided is a liquid chromatograph pump system which sucks eluent from an eluent reserving container, and which feeds pressurized high pressure eluent into a column, wherein a plunger reciprocating in a cylinder is formed on its outer peripheral surface with a stepped part along the sliding direction of the plunger in the cylinder so as to define a working chamber between the stepper part and the inner wall surface of the cylinder, the flow rate of the liquid chromatograph pump being determined by the volume of the working chamber and the traveling speed of the plunger, thereby it is possible to stably feed a liquid at an extremely low flow rate, and to satisfactorily expel air bubbles upon a start of the liquid chromatograph pump system.