An exhaust purification system of an internal combustion engine of the present invention comprises a silver-alumina-based catalyst device arranged in the engine exhaust system. When a temperature of the silver-alumina-based catalyst device becomes a second set temperature T2 lower than a first set temperature T1 at which the silver-alumina-based catalyst device releases NO2, and releases NO, the silver-alumina-based catalyst device is heated such that a temperature elevation rate thereof is increased to make the temperature T of the silver-alumina-based catalyst device be a third set temperature T3 between the first set temperature T1 and the second set temperature T2.