A regeneration method of an apparatus of purifying an exhaust gas including a catalytic converter which is disposed on an exhaust pipe and includes a lean NOx trap (LNT) device in which a first LNT catalyst is coated and a catalyzed particulate filter (CPF) in which a second LNT catalyst is coated may include determining whether a nitrogen oxide (NOx) amount absorbed in the LNT device is greater than a threshold NOx amount, determining whether a temperature of the LNT device is higher than a first predetermined temperature when the NOx amount absorbed in the LNT device is greater than the threshold NOx amount, and regenerating, both of the LNT device and the CPF or only the LNT device according to a temperature of the CPF when the temperature of the LNT device is higher than the first predetermined temperature.