A common fuel injection amount is calculated for the cylinders of a first cylinder group, which performs a rich burn process, and the cylinders of a second cylinder group, which performs a lean burn process. The calculated fuel injection amount is corrected with an air-fuel ratio learning value that is acquired beforehand during a stoichiometric operation. Intake valve lift amounts for the cylinders of the first and second cylinder groups are calculated in accordance with an engine speed and engine load. In compliance with the calculated values, a variable valve mechanism is driven, and fuel is ignited. When performing sulfur poisoning recovery of the Ox catalyst, the exhaust air fuel ratio control means change the intake air amount for each cylinder while providing substantially the same fuel injection amount for all cylinders.