An exhaust gas cleaner comprising (a) at least one filter made of a heat-resistant and electrically insulating material for trapping floating fine particles in an exhaust gas; and (b) at least a pair of electrodes stacked with the filter alternately, voltage being applied between the adjacent electrodes to burn electrically conductive and burnable fine particles trapped in the filter by heat generated by a current flowing between the adjacent electrodes, and the direction of the flow of the exhaust gas in the filter being essentially parallel to that of the laminate surface of the electrodes. The filter may carry a catalyst which functions to reduce harmful gas components in the exhaust gas.