An exhaust gas cleaner comprising a heat-resistant, porous filter, a porous ceramic layer formed on the filter, and a catalyst supported by the ceramic layer, the catalyst consisting essentially of:(a) at least one of alkali metal elements;(b) copper and vanadium; and(c) at least one of rare earth elements.By using this exhaust gas cleaner, particulate matter in the exhaust gas is oxidized by the catalyst supported by the filter, and nitrogen oxides are reduced by the particulate matter serving as a reducing agent.