To reduce a peak value of rotational load when a cam shaft and a fuel pump connected to the cam shaft are driven, in an engine for driving the fuel pump by the cam shaft.

When the cam shaft is rotated, periodic rotational load (reference to a thin slid line) is generated when a valve gear cam drives an intake valve and an exhaust valve. When a pump shaft of the fuel pump driven by the cam shaft is rotated, periodic rotational load (reference to a broken line) is generated. When a phase for coupling both of the cam shaft and the pump shaft is set so that a peak valve Fa of composed rotational load (reference to a thick solid line) of rotational load of the cam shaft and rotational load of the pump shaft may be decreased or minimum [refer to (A)], the peak value Fa can be made smaller than a peak value Fb when the phase is improperly set [refer to (B)].