Conventionally, a silver-cerium oxide composite containing a silver particle and cerium oxide covering the surface of the silver particle has been synthesized through a multi-stage process, and is disadvantageous not only in that there is a need to use an organic solvent and a surfactant, causing the time and cost to be increased, but also in that there is a possibility that fulminating silver is formed, leading to a problem about the safety. A method for producing a catalyst having a silver-cerium oxide composite and an alkaline carrier having supported thereon the oxide composite, the silver-cerium oxide composite containing a silver particle and cerium oxide covering the surface of the silver particle, the method having preparing a mixture containing a silver compound, a cerium compound, and an alkaline carrier, and drying the mixture is provided.