An exhaust-gas-purifying system of an internal combustion engine of the present disclosure sets a reduction treatment necessity flag to ON when an input gas temperature of an exhaust gas introduced into an exhaust-gas-purifying catalyst is higher than a reference temperature. Then, it is determined whether reduction treatment execution conditions in which the reduction treatment necessity flag has been set to ON and the input gas temperature has decreased and falls within a preset temperature range up to a reference temperature or lower are satisfied. Then, when it is determined that reduction treatment execution conditions are satisfied, a reduction treatment in which an air-fuel ratio of an intake gas supplied into the engine is adjusted to be richer than a stoichiometric air-fuel ratio is performed, and the reduction treatment necessity flag is set to OFF.