PURPOSE: To prevent a rapid pressure rise from occurring in a combustion chamber and reduce the quantity of a harmful exhaust gas, by injecting a fuel stepwise through a first-stage injection and a main injection.

CONSTITUTION: In the unit injector 10, a pumping plunger 12 is slidingly reciprocated in accordance with the rotation of a cam shaft 38, in which case a quantity-regulating plunger 14 is moved in accordance with the pressure generated by forcing-in of the pumping plunger 12, and by the movement of the plunger 14, the fuel charged on the downstream side of a check valve 36 is compressed, and the first-stage injection and the main injection are effected stepwise. In the main injection stage, when the plunger 14 is moved to a predetermined position, a pumping chamber 32 is communicated to a main injection cut-off port 18, thereby finishing the main injection.