An exhaust-gas-purifying system of an internal combustion engine using an exhaust-gas-purifying catalyst in which at least one of Rh, Pd, and Pt is supported on a CeO 2 -containing support, comprising: a flag ON setting unit (S201 to S203) configured to set a reduction treatment necessity flag to ON (F=1) when an input gas temperature (T IN ) which is a temperature of an exhaust gas introduced into the exhaust-gas-purifying catalyst is higher than a reference temperature (T3) that is set as a temperature at which an oxidation activity rate of the exhaust-gas-purifying catalyst is 50% or more; a conditions satisfying determination unit (S104 to S106) configured to determine whether reduction treatment execution conditions are satisfied in which the reduction treatment necessity flag has been set to ON (F=1) by the flag ON setting unit and the input gas temperature (T IN ) has decreased and falls within a preset temperature range between a lower limit temperature (T1) and an upper limit temperature (T2) that is lower than the reference temperature (T3), wherein the lower limit temperature (T1) is a threshold value preset as a temperature of a lower limit at which a reduction effect is obtained when a reduction treatment is performed and the upper limit temperature (T2) is a threshold value of a reduction temperature preset as a temperature of an upper limit in which a reduction effect is obtained when the reduction treatment is performed; a reduction treatment performing unit (S107) configured to perform a reduction treatment in which an air-fuel ratio of an intake gas supplied to the internal combustion engine is adjusted to be richer than a stoichiometric air-fuel ratio when the conditions satisfying determination unit determines that the reduction treatment execution conditions are satisfied; and a flag OFF setting unit (S304) configured to set the reduction treatment necessity flag to OFF (F=0) when the reduction treatment is performed by the reduction treatment performing unit. a flag ON setting unit (S201 to S203) configured to set a reduction treatment necessity flag to ON (F=1) when an input gas temperature (T IN ) which is a temperature of an exhaust gas introduced into the exhaust-gas-purifying catalyst is higher than a reference temperature (T3) that is set as a temperature at which an oxidation activity rate of the exhaust-gas-purifying catalyst is 50% or more; a conditions satisfying determination unit (S104 to S106) configured to determine whether reduction treatment execution conditions are satisfied in which the reduction treatment necessity flag has been set to ON (F=1) by the flag ON setting unit and the input gas temperature (T IN ) has decreased and falls within a preset temperature range between a lower limit temperature (T1) and an upper limit temperature (T2) that is lower than the reference temperature (T3), wherein the lower limit temperature (T1) is a threshold value preset as a temperature of a lower limit at which a reduction effect is obtained when a reduction treatment is performed and the upper limit temperature (T2) is a threshold value of a reduction temperature preset as a temperature of an upper limit in which a reduction effect is obtained when the reduction treatment is performed; a reduction treatment performing unit (S107) configured to perform a reduction treatment in which an air-fuel ratio of an intake gas supplied to the internal combustion engine is adjusted to be richer than a stoichiometric air-fuel ratio when the conditions satisfying determination unit determines that the reduction treatment execution conditions are satisfied; and a flag OFF setting unit (S304) configured to set the reduction treatment necessity flag to OFF (F=0) when the reduction treatment is performed by the reduction treatment performing unit. <EOS>