TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preparation (claimed): Preparation of the catalyst comprises forming catalyst particles in a conductive carrier by a sputtering method or a vapor deposition method. Preferred Components: In formula (I): an amount of tantalum having a metal bond is equal to or less than twice that of tantalum having an oxygen bond; an amount of T (where T is tungsten and/or nickel) having an oxygen bond is equal to or less than 10 times that of T having a metal bond; and an amount of T (where T is hafnium) having a metal bond is equal to or less than twice that of T having an oxygen bond, in an X-ray photoelectron spectroscopy. In formula (II), an amount of tantalum having an oxygen bond is equal to or less than twice that of tantalum having a metal bond; an amount of T (where T is molybdenum, vanadium and/or chromium) having an oxygen bond is equal to or less than 10 times that of T having a metal bond; and an amount of T (where T is niobium, zirconium and/or titanium) having a metal bond is equal to or less than twice that of T having an oxygen bond, in an X-ray photoelectron spectroscopy. The ion exchange membrane is a proton-conductive membrane. Preferred Process: The conductive carrier is kept at 400 degrees C or less during performing the sputtering method or the vapor deposition method. The method further comprises performing an acid washing treatment or a heat treatment to the catalyst particles. The acid treatment is performed with a sulfuric acid aqueous solution. The heat treatment is performed at 10-400 degrees C and under an oxygen partial pressure of less than 5%. The fuel including methanol or mixture of methanol and water is supplied to the anode. EXAMPLE - A carbon black carrier was sufficiently dispersed. The dispersed carrier was put on a holder in a chamber of an ion beam sputtering apparatus, a degree of vacuum became 3x 10-~6 Torr or less, and then argon gas flowed in. Then, the carrier was stirred to give the platinum-ruthenium-tantalum-hafnium catalyst of formula (Pt40Ru50Ta5Hf5).