To improve the startup performance at starting of a high-pressure fuel pump driven by an engine.

A fuel supply device of an engine includes a variable reduction gear installed in a power transmitting path leading from the engine to the high-pressure fuel pump. After starting cranking, a control of dropping the reduction ratio is conducted during a prescribed time after a prescribed engine speed increase is attained, and immediately after starting cranking, the speed of the fuel pump is increased by dropping the reduction ratio within the prescribed time while the cranking torque is lowered without dropping the reduction ratio and thereby the vibration is suppressed, whereby the fuel pressure is raised quickly so as to quicken the start of the fuel injection with a high fuel pressure.