PURPOSE: To use a fuel injection pump for also a multicylinder internal combustion engine by unrotatably coupling a second stroke plate holding end face cams of the same number with a drive shaft and rotatably holding a second traveling roller rolling on the end face cam of the second stroke plate within a roller holding body movable in an axial direction.

CONSTITUTION: This pump is constituted of a first stroke plate 26 which is unrotatably coupled with a pump piston 13, a first traveling roller 28 rolling on this stroke plate 26, a second stroke plate 27 which is unrotatably coupled with a drive shaft 15 and a second traveling roller 29 rolling on this plate 27. The traveling rollers 28, 29 are provided within two planes shifted in an axial direction within a roller holding body 30 and the roller holding body 30 is held coaxially with the drive shaft 15 so as to be unrotatable within a casing 11 and movable in an axial direction. Each stroke plate 26, 27 has end face cams 31, 32 of numbers corresponding to cylinders, stroke motion of the pump piston 13 is generated at the time of rotation of each stroke plate 26, 27 and stroke is stipulated by the total of end face cam heights of the stroke plates 26, 27.