To increase pressure in a short time up to required fuel pressure when an engine is in the cranking revolution, and insure excellent stability even when the engine is started at the time of low temperature where the amount of required fuel is greatly demanded.

A high pressure fuel pump 1 is connected with a cam shaft 7 by way of a variable speed gear 11. Signals are inputted from a starter switch 14 acting as a detecting means when an engine is started, a fuel pressure sensor 15 acting as an injection valve supplied fuel pressure detecting means and a crank angle sensor 16, at the time of engine starting based on these signals an actuator 12 is driven, and the variable speed gear 11 is switched over to its speed increasing side, and when duel pressure becomes greater than a specified value, or it is judged by an engine start completion judging means that engine starting has been completed, the actuator is thereby driven, and the variable speed gear 11 is so switched over that the revolving speed of the high pressure fuel pump coincides with that of the camshaft.