Abstract: During a shut-down period of an engine based on an idle stop control, a computer estimates a power stroke cylinder and a compression stroke cylinder when the engine is stopped. A fuel is injected into the power stroke cylinder and the compression stroke cylinder in an intake stroke just before the engine is stopped. An air-fuel mixture is hold in each cylinder with the engine stopped. When an auto start is required while the engine is stopped, a spark ignition is performed in the power stroke cylinder to start cranking of the engine by combustion energy. At nest ignition timing, a spark ignition is performed in the compression stroke cylinder to start the engine without an aid of a starter.