An exhaust gas control apparatus for an internal combustion engine, the exhaust gas control apparatus comprising: an exhaust gas control catalyst disposed in an exhaust passage of the internal combustion engine, the exhaust gas control catalyst having a catalytic function; a particulate filter disposed in the exhaust passage at a location downstream of the exhaust gas control catalyst in an exhaust gas flow direction; an oxygen supply device configured to supply gas containing oxygen into exhaust gas flowing into the particulate filter at a location downstream of the exhaust gas control catalyst in the exhaust gas flow direction; a catalyst temperature sensor; characterized in that the exhaust gas control apparatus comprises an electronic control unit configured to regulate an amount of oxygen that is supplied from the oxygen supply device, when a temperature of the exhaust gas control catalyst is detected by the catalyst temperature sensor as falling within a predetermined temperature range higher than or equal to an activation temperature, an amount of particulate matter deposited on the particular filter is greater than a minimum allowable value, and an air-fuel ratio of exhaust gas emitted from a body of the internal combustion engine is a rich air-fuel ratio richer than a stoichiometric air-fuel ratio, the electronic control unit being configured to cause the oxygen supply device to supply oxygen into the exhaust gas while periodically increasing or reducing the oxygen such that an air-fuel ratio of exhaust gas flowing into the particulate filter alternately varies between the rich air-fuel ratio and a lean air-fuel ratio leaner than the stoichiometric air-fuel ratio, wherein the predetermined temperature range is higher than or equal to 400°C and lower than or equal to 600°C, wherein the electronic control unit is configured to increase a leanness degree at the time when the air-fuel ratio of exhaust gas flowing into the particulate filter is the leanest as a temperature of the particulate filter decreases, and wherein if the temperature of the exhaust gas control catalyst is detected by the catalyst temperature sensor as being less than the activation temperature, the electronic control unit is configured to start a temperature raising process to increase the temperature of the exhaust gas control catalyst. an exhaust gas control catalyst disposed in an exhaust passage of the internal combustion engine, the exhaust gas control catalyst having a catalytic function; a particulate filter disposed in the exhaust passage at a location downstream of the exhaust gas control catalyst in an exhaust gas flow direction; an oxygen supply device configured to supply gas containing oxygen into exhaust gas flowing into the particulate filter at a location downstream of the exhaust gas control catalyst in the exhaust gas flow direction; a catalyst temperature sensor; characterized in that the exhaust gas control apparatus comprises an electronic control unit configured to regulate an amount of oxygen that is supplied from the oxygen supply device, when a temperature of the exhaust gas control catalyst is detected by the catalyst temperature sensor as falling within a predetermined temperature range higher than or equal to an activation temperature, an amount of particulate matter deposited on the particular filter is greater than a minimum allowable value, and an air-fuel ratio of exhaust gas emitted from a body of the internal combustion engine is a rich air-fuel ratio richer than a stoichiometric air-fuel ratio, the electronic control unit being configured to cause the oxygen supply device to supply oxygen into the exhaust gas while periodically increasing or reducing the oxygen such that an air-fuel ratio of exhaust gas flowing into the particulate filter alternately varies between the rich air-fuel ratio and a lean air-fuel ratio leaner than the stoichiometric air-fuel ratio, wherein the predetermined temperature range is higher than or equal to 400°C and lower than or equal to 600°C, wherein the electronic control unit is configured to increase a leanness degree at the time when the air-fuel ratio of exhaust gas flowing into the particulate filter is the leanest as a temperature of the particulate filter decreases, and