When a stop position of a piston resulting from the automatic stop is in a range that is on an advance side of a threshold in terms of crank angle, fuel injection is performed at beginning of the automatic restart-up in the cylinder that is in the intake stroke and an ignition is performed in a subsequent initial compression stroke in the same cylinder. When the stop position of the piston resulting is in a range that is on a retard side of the threshold in terms of crank angle, initial fuel injection is performed in the cylinder that next enters an intake stroke among the cylinders of the internal combustion engine after the beginning of automatic restart-up and initial ignition is performed in a subsequent compression stroke in the same cylinder. The threshold is determined in accordance with an amount of deviation of a crank angle.