To arbitrarily set injection supply time for subfuel in a distribution type fuel injection pump 9 performing an injection supply for subfuel before an injection supply for main fuel to each cylinder 2, 3, 4 in an internal combustion engine 1 such as a multicylinder diesel engine.

A plunger 12 is constituted so as to be reciprocated only one time by auxiliary cam 29 separate from a cam 28 during each reciprocating by the cam 28. In each part on this side by a proper angle θ for the rotating direction of the plunger 12 from each delivery port 32, 33, 34 of a plunger barrel 13, auxiliary delivery ports 35, 36, 37 communicated with the distribution port 21 during forward movement by the auxiliary cam 28 of the plunger 12 are provided so as to be communicated with one delivery port located on the rear side for the rotating direction of the plunger 12 from the auxiliary delivery ports 35, 36, 37 of each delivery port 32, 33, 34.