An exhaust purification system of an internal combustion engine, which includes: a silver-alumina-based catalyst, which is arranged in an engine exhaust system and, when an air-fuel ratio of exhaust gas is leaner than a stoichiometric air-fuel ratio, releases adsorbed NO2 at a first set temperature and adsorbed NO at a second set temperature, a secondary air feed passage configured to suppress a temperature rise of the silver-alumina-based catalyst; and an electronic control unit, that: controls the air flow through the secondary air feed passage to: when the silver-alumina-based catalyst has reached a third set temperature, suppress a temperature rise of the silver-alumina-based catalyst to maintain the silver-alumina-based catalyst near the third set temperature, and then lift the suppression of the temperature rise of the silver-alumina-based catalyst so that at least part of the NO adsorbed at the silver-alumina-based catalyst, is oxidized to NO2 to be adsorbed at the silver-alumina-based catalyst.