An air-purifying filter includes a carrier base and a TiO.sub.2 -Pd composite catalyst supported on the carrier base. CO in air treated by the filter is adsorbed onto the Pd surface and thus decomposed by oxidization to CO.sub.2, whereas sulfur compounds in the air are adsorbed onto the Pd surface and then transferred to the TiO.sub.2 surface where they are decomposed by oxidization to SO.sub.4.sup.-2 when the TiO.sub.2 is subjected to irradiation. Preferably, Pd exists in a relatively small quantity at a first side of the carrier base in the vicinity of a light source and in a greater quantity at a second side opposite the first side. The first side is preferably located upstream relative to flow of air treated by the filter. An air-purifier utilizing this filter is mounted in an automobile, preferably on a rear shelf or in a trunk compartment. The air-purifier has a light source for irradiating the filter, and an exhaust port, arranged at a position to utilize negative pressure of the automobile generated during driving, to exhaust any substances desorbed from the composite catalyst to the outside of the automobile.