A method for controlling an exhaust gas purification apparatus according to an exemplary embodiment of the present invention is to improve performance of a three-way catalyst (TWC) purifying exhaust gas exhausted from an engine and includes determining heat load of the three-way catalyst by use of a temperature sensor and an exhaust gas flow rate sensor; measuring oxygen storage capacity (OSC) stored in the three-way catalyst according to the heat load; determining an inflection point by use of change amount of the OSC; and controlling catalyst heating period differently around the inflection point.