An injection pump includes a rotor (10) having a central axial bore (48) and a radial bore (16) and rotated in relationship with an engine. A free piston (46) reciprocably inserted in the central axial bore (48) defines a first and second chamber (44, 50). The first chamber (44) includes a plurality of first radial passages (58-68) and a radial spill port (56) and communicates with the radial bore (16) and the second pressure chamber (50) includes a plurality of second radial passages (72) and a discharge passage (54). A pair of plungers (12, 14) which is disposed in the radial bore (16) is so constructed as to produce, in accordance with the revolution of the rotor (10), a compression period in which the liquid fuel is pressurized in the first pressure chamber (44) and pressurized fuel in the second pressure chamber (50) is supplied to the engine through the discharge passage (54), and a suction period in which the liquid fuel is supplied to the pressure chambers (44, 50).