The objective of the present invention is to prevent an increase in the amount of oxygen stored in a catalyst due to a fuel cut by performing a rich spike, even when the fuel is again supplied after a fuel cut in some of the cylinders. When a prescribed fuel cut condition has been satisfied (t1, t6), first, the fuel to some of the cylinders is cut, and after a prescribed period of time (A1) has elapsed, the supply of fuel to all of the cylinders is cut (A2). When the fuel to only some of the cylinders has been cut and a prescribed fuel cut recovery condition has been satisfied (t3), fuel is again supplied to the aforementioned cylinders, and during a prescribed period (C1) after the supply of the fuel has been restarted a rich spike (D1) is executed, whereby the amount of fuel being supplied is increased and the exhaust air-fuel ratio is controlled so as to be richer than the stoichiometric air-fuel ratio.