A system for purifying an exhaust gas includes an engine, a lean NOx trap (LNT) mounted on the exhaust pipe, a dosing module mounted at the exhaust pipe downstream of the LNT, a selective catalytic reduction (SCR) catalyst mounted at the exhaust pipe downstream of the dosing module, and a controller for performing a denitrification (DeNOx) share between the LNT and the SCR catalyst according to a driving condition of the engine, wherein the controller predicts a NOx purifying ratio of the SCR catalyst according to the driving condition of the engine and adjusts a regeneration efficiency of the LNT based on an actual NOx purifying ratio of the SCR catalyst.