An internal combustion engine wherein an SOx trap catalyst (12), an NOx storage catalyst (14), and a fuel addition valve (15) are arranged in an engine exhaust passage. When making the air-fuel ratio of the exhaust gas flowing into the NOx storage catalyst (14) the stoichiometric air-fuel ratio or rich so as to make the NOx storage catalyst (14) release NOx, additional fuel is supplied into the combustion chamber (2) and fuel is added from the fuel addition valve (15). At this time, the amount of additional fuel to the combustion chamber (2) is controlled so that the air-fuel ratio of the exhaust gas exhausted from the combustion chamber (2) becomes the smallest in the range where the SOx trap catalyst (12) does not release SOx.