PURPOSE: To increase the responsiveness at the time of stop by forming a control face extending obliquely on a peripheral face of a distributor piston and rotating and displacing the distributor piston in accordance with the travel in the axial direction to reduce a travel amount of the distributor piston for stopping an internal combustion engine.

CONSTITUTION: This injection pump drives a feed pump 3 by a drive shaft 2 driven by an engine and rotates a cam ring 5 by a cuplike entraining part 4 interlocked with the drive shaft 2. A piston 8 is reciprocated by the rotation of the cam ring 5, and fuel in a pump chamber 19 is pressurized and is distributed and supplied to an injection nozzle 24 through a distributor piston 14, etc. The distributor piston 14 is rotated integrally with the entraining part 4 by an entraining finger 15 and is displaced in the axial direction in accordance with pressure in a control chamber 35. In this case, a control face 51 extended obliquely on a peripheral face of the distributor piston 14 is formed to rotate and displace the distributor piston 14 in accordance with the travel in the axial direction thereof, and an overlap amount of a suction longitudinal groove 25 and a suction passage 26 can be changed.