A method for controlling an exhaust gas purification apparatus as a catalyst oxygen purge control method during a cold engine period of an exhaust gas purification apparatus including a three way catalyst (TWC) converter purifying exhaust gas exhausted from the engine includes determining whether a fuel cut condition of an injector which injects the fuel to the combustion chamber is satisfied; performing a fuel cut of the injector when the fuel cut condition is satisfied; determining heat load of the three way catalyst by use of a temperature detector and an exhaust gas flow rate detector; measuring oxygen storage capacity (OSC) stored in the three way catalyst according to the heat load; determining an inflection point by use of variation amount of the OSC; and controlling oxygen purge period differently around the inflection point.