Catalyst for producing dimethyl ether, method for producing catalyst and method for producing dimethyl ether

A catalyst for producing dimethyl ether which comprises alumina particles having an average size of 200 μm or less and a methanol synthesis catalyst layer formed around the alumina particles. The methanol synthesis catalyst is in an amount of 0.05 to 5 parts by weight to 1 part by weight of the alumina particles. Dimethyl ether is produced by the method of forming a slurry by introducing the catalyst into a solvent and introducing a mixed gas comprising carbon monoxide and hydrogen into the slurry.