Even though a pump head part is finally fixed to a pump body with a fixing member, the pump head part is movable relative to the pump body perpendicular to the axial direction of a plunger at a stage before the pump head part is fixed with the fixing member. In this state, if a plunger driving part is moved to a predetermined location on the front end side of the pump body and the pump head part and the plunger driving part are fitted to each other, the pump head part is positioned where the center axis of the plunger and the center axis of the pump chamber are substantially aligned. By fixing the pump head part to the pump body with the fixing member at this location, it is possible to assemble a plunger pump with the center axis of the plunger and the center axis substantially aligned.