Exhaust Purification Device of Internal Combustion Engine

An exhaust purification device of an internal combustion engine arranging in an engine exhaust passage an SOx trap catalyst able to trap SOx contained in exhaust gas and arranging in the exhaust passage downstream of the SOx trap catalyst an NOx storage catalyst storing NOx contained in the exhaust gas when an air-fuel ratio of an inflowing exhaust gas is lean and releasing a stored NOx when the air-fuel ratio of the inflowing exhaust gas becomes the stoichiometric air-fuel ratio or rich, wherein a fuel addition valve for adding fuel is arranged in the engine exhaust passage upstream of the NOx storage catalyst, and when making the air-fuel ratio of the exhaust gas flowing into the NOx storage catalyst the stoichiometric air-fuel ratio or rich to make the NOx storage catalyst release the NOx, an additional fuel is fed into the combustion chamber and a fuel is added from the fuel addition valve, and at this time, the amount of additional fuel to the combustion chamber and the amount of added fuel from the fuel addition valve are controlled so that the air-fuel ratio of the exhaust gas exhausted from the combustion chamber becomes the smallest in the range where the SOx trap catalyst does not release SOx.