An apparatus for efficiently purifying NOx in the exhaust gas or soluble organic substance in the exhaust gas from a diesel engine. A plurality of purification units are arranged in a housing, each of which is composed of a catalytic layer for reducing NOx and a cooling core for cooling the exhaust gas admitted through the catalytic layer. The multi-staged purification units are so constructed to admit the exhaust gas to flow therethrough. The catalytic layer in the form of a porous carrier such as a honeycomb structure carries catalytic components. Upon purifying soluble organic substance in the exhaust gas from a diesel engine, the catalytic components carried on the catalytic layer serve to efficiently purify such substance, as well as inhibiting the reaction to form sulfate.