An apparatus for purifying exhaust gas includes: an engine; an exhaust gas air-fuel ratio adjustor for adjusting an air-fuel ratio of the exhaust gas; a lean NOx trap (LNT) mounted on the exhaust pipe and generating ammonia or reducing nitrogen oxides or desorbed nitrogen oxides contained in the exhaust gas using a reducing agent including carbon monoxide, hydrocarbon, or hydrogen contained in the exhaust gas; a three way catalyst (TWC) mounted on the exhaust pipe at a rear end of the LNT, and converting noxious gas in the exhaust gas into harmless components through a redox reaction; and a controller controlling the air-fuel ratio of the exhaust gas to a stoichiometric air-fuel ratio when the nitrogen oxide storage or purification performance of the LNT is in the operating period of the engine less than a predetermined level.