PURPOSE: To provide a distributor type fuel injection pump which can effectively control injection rate according to the operation state of an engine without using a valve and an accessary.

CONSTITUTION: A distributor type fuel injection pump is provided with a by-pass passage (a by-pass hole 27, a by-pass groove 33, a communicating hole 31) to leak a pressure feed fuel before a cutoff port 21 is opened, and a member 29 which moves in a body with a control sleeve 22 to block up the by-pass hole 27 when the control sleeve 22 moves in a direction where the quantity of injection enlarges (a position to which the control sleeve 22 is moved at the time of starting and of heavy load at low speed).