An apparatus is provided which includes an internal combustion engine (1) of a lean-burn type, an NOx catalyst (46) disposed in an exhaust passage of the engine so as to remove nitrogen oxides contained in exhaust gas emitted from the engine, and a variable valve control system (30, 31, 30a, 31a) capable of changing the opening and closing timing and/or a lift of the intake valve and/or the exhaust valve for each cylinder of the engine. The variable valve control system is controlled so that the exhaust gas to which the NOx catalyst is exposed is controlled so as to be suitable for removing a selected gaseous component from the NOx catalyst when the selected gaseous component should be removed. A method of purifying an exhaust gas emitted from the above engine is also provided.