An apparatus for, and a method of, purifying exhaust gas emitted from an internal combustion engine reduces fuel consumption under a lean operating condition and generates high torque under a rich operating condition without deteriorating the cleanness of exhaust gas and the driveability of the engine. The apparatus and method improve the durability of a variable valve timing mechanism of the engine. The engine operation involves lean and rich operating conditions. The variable valve timing mechanism of the apparatus changes the open and close timing of at least one of intake and exhaust valves of the engine. The apparatus further has a catalytic converter in an exhaust system, to occlude NOx under the lean operating condition and discharge and reduce the occluded NOx under the rich operating condition. The apparatus also has a prohibition unit for prohibiting the variable valve timing mechanism from changing the valve open and close timing of the valves when the air-fuel ratio of the engine is changed from lean to rich to discharge and reduce the occluded NOx.