a distributor type fuel injection pump which includes a port formed within the pressurized fuel distributing plunger with one end thereof communicating with the pump working chamber and the other end terminating in the outer periphery of said plunger , and a relief passage having one end thereof terminating in the inner peripheral wall of the plunger barrel and the other end communicating with a zone under a lower pressure . said port and relief passage are so located as to register with each other at the beginning of the fuel delivery stroke of said plunger , and said relief passage is so arranged as to be permanently kept closed by a valve means which is actuated by a valve actuating means for actuating said valve means in response to a fuel supply pressure varying as a function of the engine rotational speed , except in a predetermined low engine speed range , to obtain a decreased injection rate during idling so as to increase the injection period , thereby reducing the rate of combustion of the engine to largely reduce the combustion noise .