A simple structured high-pressure fuel pump.A fuel pump comprises a reciprocably-supported cylinder, a pressurizing chamber using part of the outer surface of the cylinder as the wall surface which move to change the internal volume, a fuel intake passage forming a fuel passage which introduces fuel to the pressurizing chamber, a fuel discharge passage for the compressed fuel coming out from the pressurizing chamber. A fuel intake valve is provided in fuel intake passage. A fuel discharge valve is provided in said fuel discharge passage. A connecting passage connects upstream side of the intake valve in the fuel intake passage and the downstream side of it. A check valve which flows fuel from the fuel discharge flow passage to the fuel intake passage is provided in the connecting passage.