A method of producing dimethyl ether by catalytic dehydration of crude methanol as feedstock in the gas phase includes providing the crude methanol from methanol synthesis, where the crude methanol having a total content of carbonyl compounds of not more than 100 wt-ppm, calculated, as mass equivalents of acetone. The crude methanol is evaporated, and the reaction temperature and reaction pressure are adjusted. A reactor filled with dehydration catalyst is charged with the evaporated crude methanol with a defined space velocity. A gaseous product mixture comprising dimethyl ether, non-reacted methanol and water is discharged. Cooling, partial condensation and separation of the gaseous product mixture are carried out so as to provide gaseous dimethyl ether, liquid water and methanol as products, and the methanol is recirculated.