PURPOSE: To provide the accumulator fuel injection device of a Diesel engine capable of satisfactorily controlling the fuel injection quantity at the time of a start without complicating the structure of the Diesel engine.

CONSTITUTION: When the engine revolving speed NE of a Diesel engine is less than a prescribed value (step 103: yes) and the temperature of the cooling water is less than a prescribed value (step 105: yes) at the time of a start, drive pulses are continuously outputted to an injector in the combustion stroke (step 175). The injector injects a quantity of fuel corresponding to the pressure feed quantity of a fuel feed pump. The fuel feed pump is controlled based on the target fuel injection quantity QS (step 177). The fuel injection quantity can be satisfactorily controlled even at the time of a start when the actual common rail pressure PA is low.