The present invention relates to a silver catalyst for producing an epoxy compound through epoxidation of an olefin, and a preparation method thereof, wherein the mass content of gallium in the silver catalyst is 10-5000 ppm, and the mass content of silver in the silver catalyst is 10-50%. The preparation method comprises: impregnating an alpha-alumina carrier by using a solution containing an organic amine, a silver-containing compound, a gallium-containing compound auxiliary agent, an alkali metal compound auxiliary agent, an alkaline earth metal compound auxiliary agent, a group VIIB metal compound auxiliary agent and a group VIB metal compound auxiliary agent, leaching, and activating to obtain the silver catalyst. The invention further relates applications of the silver catalyst in production of epoxy compounds through epoxidation of olefins, wherein particularly the silver catalyst shows good selectivity, good activity and good stability in the ethylene oxide production reaction through epoxidation of ethylene.