A stop and start control apparatus of an internal combustion engine prevents fuel supplied in a specific cylinder at the time of stopping the engine from being discharged in an unburned state. When an ignition switch is turned off in a state that the unburned fuel is sealed in the combustion chamber of a specific cylinder during idling stop, the unburned fuel is combusted to prevent the unburned fuel from being discharged. The vibration occurring at that time can be suppressed by rotating the motor generator in the counter direction to the rotation direction of the crankshaft. After the unburned fuel is sealed in the combustion chamber of the specific cylinder, if it is estimated that the unburned fuel is discharged, the exhaust valve corresponding to the specific cylinder is closed at the predetermined timing, or the unburned fuel is combusted, whereby the unburned fuel is prevented from being discharged. Thus, deterioration of emission can be avoided.