A catalyst (9) is disposed in an exhaust passage (8) of an internal combustion engine (1) for trapping nitrogen oxides in the exhaust from a fuel mixture of a lean air-fuel ratio and reducing trapped nitrogen oxides in the exhaust from a fuel mixture of an air-fuel ratio other than the lean air-fuel ratio. The catalyst (9) also traps sulfur oxides in the exhaust when the catalyst temperature is less than a predetermined temperature, and discharges the trapped sulfur oxides when the catalyst temperature rises above the predetermined temperature. A microprocessor (10) calculates for example the sulfur oxide stored amount of the catalyst (9) based on engine running conditions, and determines that sulfur oxide discharge condition is satisfied when the sulfur oxide stored amount exceeds a predetermined amount. When the discharge condition is satisfied, the microprocessor (10) controls the fuel injection amount and fuel injection timing of the fuel injector (6) so as to generate a stratified air-fuel mixture in the combustion chamber (3). The stratified air-fuel mixture comprises a first layer surrounding the spark plug (7) and a second layer situated outside the first layer. The first layer comprises an atomized air-fuel mixture of a rich air-fuel ratio within an ignitable range. The second layer is leaner than the first layer.