To maintain the good lubricating state of a plunger and prevent malfunction.

In a face cam distribution type fuel infection pump 1, a plunger 14 rotating and reiprocating synchronously with the operation of an engine is housed in a cylinder 11 disposed in a pump head 9. When the plunger 14 reciprocates, fuel is sucked to a pump high pressure chamber 17 and the fuel is compressed. Then, when a solenoid valve 30 is driven at a prescribed timing, the compressed fuel of the pump high pressure chamber 17 spills. In this case, the timing of fuel intake and the timing of fuel spill are adjusted by driving the solenoid valve 30 every injection of each cylinder of the engine. The plunger 14 is provided with a groove part 26 extending in the axial direction of the plunger from the pump high pressure chamber 17. Thus, a lubricating operation is applied to a slide surface between the inner wall of the cylinder 11 and the plunger 14 by the fuel entering the groove part 26.