Abstract: A catalyst for cleaning exhaust fumes is disclosed, comprised of a catalyst ingredient of a base metal hyperfine powder of iron, nickel, or the like produced by the vaporization in gas, or their mixture, and a ceramic catalyst carrier of .gamma. (gamma) - alumina, titanium oxide, or the like, the catalyst ingredient being set on a ceramic catalyst carrier. This catalyst has high activity and the ability to remain stable over a long period of time. Furthermore, this catalyst has a new effect provided by hyperfining of particles, and a new physical or chemical characteristic indicated as a result of mixing them.