An injection pump includes a rotor having a central axial bore and a radial bore and rotated in relationship with an engine. A free piston reciprocably inserted in the central axial bore defines a first and second chamber. The first chamber includes a plurality of first radial passages and a radial spill port and communicate with the radial bore and the second pressure chamber includes a plurality of second radial passages and a discharge passage. A pair of plungers which is disposed in the radial bore is so constructed as to produce, in accordance with the revolution of the rotor, a compression period in which the liquid fuel is pressurized in the first pressure chamber and pressurized fuel in the second pressure chamber is supplied to the engine through the discharge passage, and a suction period in which the liquid fuel is supplied to the pressure chambers.