PURPOSE: To perform injection of fuel even when a rotation signal is not inputted during starting and when a sensor is failed in operation and to suppress the generation of block smoke owing to an excessive injection amount.

CONSTITUTION: In a distribution type fuel injection pump for a diesel engine, a second overflow passage 44 is branched in the middle of an overflow passage 24 running from a pump chamber 18 and communicated with a housing and a constant pressure valve 46 and a solenoid valve 48 are disposed in series in the second overflow passage 44. When an engine rotation signal is not inputted to a control circuit 30, a solenoid valve 26 is maintained in a closed state, a low water temperature state is eliminated, and the solenoid valve 48 of the overflow passage 44 is closed. The set pressure of the constant pressure valve 46 is higher than the opening pressure of a delivery valve 22 and set to a given value lower than a maximum pressure during injection of a whole amount. Thus, a whole amount is not injected but necessary fuel can be injected and ensurance of startability and reduction of the generation of black smoke are made compatible with each other.