Engine air-fuel ratio controlling means is provided to control an exhaust air-fuel ratio that is the ratio between the air contained in the exhaust gas discharged from the engine and the fuel element contained in the same exhaust gas and acting as a reducing agent at a NOx catalyst by controlling the air-fuel ratio of the gas combusted in the engine. Fuel adding means is provided upstream of the NOx catalyst in an exhaust passage to add fuel into the exhaust gas. During the SOx poisoning recovery control, when developing a state enabling SOx reduction reactions, the exhaust gas air-fuel ratio of the exhaust gas discharged from the engine and the amount of fuel added from the fuel adding means are controlled to minimize the sum of the amount of fuel injected in the engine and the amount of fuel added from the fuel adding means.