A control method for a vehicular internal combustion engine system including an internal combustion engine and an electric intake air supply device, wherein the internal combustion engine is structured to be shifted into a stoichiometric combustion mode in which a target air fuel ratio is set to a stoichiometric air fuel ratio, and a lean combustion mode in which the target air fuel ratio is set lean, and wherein the electric intake air supply device is structured to be driven by an on-vehicle battery, and employed to contribute a part of intake air quantity at least under a specific operating condition when in the lean combustion mode, the control method comprising: predefining a stoichiometric combustion operation region employing the stoichiometric combustion mode and a lean combustion operation region employing the lean combustion mode, with respect to a torque (Te) and a rotation speed (Ne) of the internal combustion engine as parameters; characterized in that the control method further comprises: determining a requested electric energy of the electric intake air supply device for a shift into the lean combustion mode in response to a shift from the stoichiometric combustion operation region into the lean combustion operation region; and continuing the stoichiometric combustion mode, without operation of the electric intake air supply device, when the on-vehicle battery is in an insufficient state of charge with respect to the requested electric energy; and setting the requested electric energy in accordance with a break-even point in duration of the lean combustion mode for a situation including a shift from the stoichiometric combustion mode to the lean combustion mode and a following shift from the lean combustion mode to the stoichiometric combustion mode, wherein an increase in fuel quantity required to treat NOx generated during the situation, and a decrease in fuel quantity caused by employment of the lean combustion mode during the situation are in balance at the break-even point. predefining a stoichiometric combustion operation region employing the stoichiometric combustion mode and a lean combustion operation region employing the lean combustion mode, with respect to a torque (Te) and a rotation speed (Ne) of the internal combustion engine as parameters; characterized in that the control method further comprises: determining a requested electric energy of the electric intake air supply device for a shift into the lean combustion mode in response to a shift from the stoichiometric combustion operation region into the lean combustion operation region; and continuing the stoichiometric combustion mode, without operation of the electric intake air supply device, when the on-vehicle battery is in an insufficient state of charge with respect to the requested electric energy; and determining a requested electric energy of the electric intake air supply device for a shift into the lean combustion mode in response to a shift from the stoichiometric combustion operation region into the lean combustion operation region; and continuing the stoichiometric combustion mode, without operation of the electric intake air supply device, when the on-vehicle battery is in an insufficient state of charge with respect to the requested electric energy; and setting the requested electric energy in accordance with a break-even point in duration of the lean combustion mode for a situation including a shift from the stoichiometric combustion mode to the lean combustion mode and a following shift from the lean combustion mode to the stoichiometric combustion mode, wherein an increase in fuel quantity required to treat NOx generated during the situation, and a decrease in fuel quantity caused by employment of the lean combustion mode during the situation are in balance at the break-even point.