A lean NOx reduction catalyst capable of reducing NOx through reaction of H.sub.2 with NOx at low temperatures below 350.degree. C. is installed in a downstream portion of an exhaust pipe of an internal combustion engine in or near a muffler. Such an NOx reduction catalyst comprises, for example, Pt/zeolite catalyst. An H.sub.2 generator is installed so as to supply the H.sub.2 to an inlet side of the NOx reduction catalyst. The H.sub.2 generator may include a reforming catalyst for reforming methanol, LPG, or natural gas to generate H.sub.2. The generated H.sub.2 flows to the NOx reduction catalyst where it reacts with NOx to purify the exhaust gas.