The exhaust purification system of an internal combustion engine comprises a catalyst 20 arranged in an exhaust passage and able to store oxygen, and an air-fuel ratio control device configured to control an air-fuel ratio of inflowing exhaust gas flowing into the catalyst. The catalyst has a precious metal and the precious metal has a property of a vapor pressure at a predetermined temperature becoming lower when oxidized. If a temperature of the catalyst is equal to or greater than a threshold temperature or if predicting a rise in temperature of the catalyst, the air-fuel ratio control device is configured to make the air-fuel ratio of the inflowing exhaust gas leaner than a stoichiometric air-fuel ratio so that an oxygen storage amount of the catalyst becomes equal to or greater than an upper side reference amount.