A control apparatus for controlling to supply of electric power to both a glow plug and a starter from a power source, the starter assisting start of the engine by using the glow plug, is provided. The control apparatus comprises a starter switch, starter, a detecting device detecting a state of the engine, a calculating circuit calculating a pre-glow time, an after-glow time, and a delay time. These times depend on both the detected state of the engine detected by the detecting device and a timing when the starter switch is turned on to a power-on position thereof. The control circuit controls the supply of the electric power to both the glow plug and the starter based on the delay time, the pre-glow time, and the after-glow time.