Hydrogen gas from a hydrogen generator which creates hydrogen gas by the electrolysis of water or water vapor is supplied at the entrance to a catalyzer provided in an exhaust line. The catalyzer performs a catalytic reaction between hydrogen gas and nitrogen oxides to achieve decomposition into nitrogen gas and water vapor in the exhaust from an internal combustion engine. The nitrogen oxides are directly reduced with said hydrogen gas in a low temperature atmosphere not higher than 350.degree. C. to achieve efficient reduction in the nitrogen oxides. The improved method and apparatus provide a catalytic system with which the nitrogen oxides in the exhaust from a lean burnt engine or a diesel engine can be effectively reduced irrespective of the concentration of oxygen gas in the exhaust without impairing the good fuel economy of those engines.