A catalyst for producing alkylene oxide including fine metal silver particles dispersed and supported on a carrier, wherein not less than 90% of the fine metal silver particles have silver particle diameters of 2 to 100 nm, is disclosed. The catalyst can be produced by impregnating a carrier with a liquid containing a silver compound or a silver ion; drying the carrier; and then irradiating the carrier with microwave to form fine metal silver particles in dispersed state on the carrier. This catalyst is used for producing olefin oxide by contact gas-phase oxidation of olefin by a molecular-oxygen-containing gas.