A fuel injection pump comprises a rotor disposed in a housing and having a pressure chamber therein, a free piston disposed slidably in the pressure chamber dividing the chamber two pump chambers, two solenoid valves for controlling fuel supply, and two preparatory chambers for metering fuel to be fed to the pump chambers. The preparatory chambers and the solenoid valves are arranged in the same plane crossing the axis of the rotor to align with each other. Fuel from a feed pump transfers to the preparatory chamber through the solenoid valve and is metered there. The metered fuel is fed to the pump chamber, pressurized there and delivered to the engine.