An exhaust cleaning method and exhaust cleaning apparatus for an internal combustion engine (1) in which a fuel is fed and burned under periodical rich/lean combustion conditions. In a fuel reformer (18) disposed independently of an exhaust channel (11) in the engine (1), the fuel for the internal combustion engine (1) is reformed to produce a reformed gas containing carbon monoxide. The reformed gas is supplied to the exhaust to be introduced into an exhaust converter (17) having, disposed therein, a catalyst which adsorbs and reduces nitrogen oxides. The nitrogen oxides contained in the exhaust gas are adsorbed and reduced. Thus, the nitrogen oxides contained in the exhaust are removed at a high efficiency.