An alkaline-earth metal compound-containing zeolite catalyst composed of a composite material comprising at least a first component, a second component, and a third component. The first component is composed of at least one of zeolites selected from a group consisting of proton-type zeolites and ammonium type zeolites. The second component is composed of at least one of alkaline-earth metal compounds. The third component is composed of at least one selected from a group consisting of aluminum oxides, aluminum hydroxides, silicon oxides, silicon hydroxides, and clay minerals. The first component has a molar ratio of Si/Al of 10 or more and 300 or less. Content of the second component relative to the first component is 0.3 mass % or more and less than 10 mass % as alkaline-earth metal. Content of the third component relative to the first component is 15 mass % or more and 200 mass % or less.