An internal combustion engine fuel pump having at least one cylinder, in which a variable-volume pump chamber is defined; a movable piston defining the bottom of the pump chamber; at least one intake valve communicating with the pump chamber; at least one delivery valve communicating with the pump chamber; and a hydraulic/pneumatic actuating device for moving the piston back and forth with respect to the cylinder to cyclically vary the volume of the pump chamber; the hydraulic/pneumatic actuating device has a first actuating chamber located beneath the pump chamber, a second actuating chamber located above the first actuating chamber, and a control member for cyclically filling the first actuating chamber with pressurized oil.