An apparatus for purifying an exhaust gas includes an engine, an exhaust pipe, a first lean NOx trap (LNT) adapted to absorb nitrogen oxide (NOx) contained in the exhaust gas, to release the absorbed NOx, and to reduce the NOx contained in the exhaust gas or the released NOx or to generate ammonia (NH3), a second LNT adapted to absorb the NOx, to release the absorbed NOx, and to reduce the NOx contained in the exhaust gas or the released NOx or to generate the NH3, and a selective catalytic reduction (SCR) catalyst adapted to temporarily absorb the NH3 and to reduce the NOx contained in the exhaust gas, wherein the second LNT is positioned such that an average temperature of the second LNT is lower than that of the first LNT by 50-150° C. based on an average temperature of the exhaust gas.