A method and apparatus for treating gas by irradiation with an electron beam. Flue gas discharged from a fuel combustion facility is treated with an electron beam to remove sulfur oxides and/or nitrogen oxides. Ammonia is added to the flue gas and the mixed gas is irradiated with an electron beam in a process vessel. A dust collector receives the gas and collects a by-product mainly composed of ammonium sulfate and/or ammonium nitrate which is produced by the reaction in the process vessel. A gas-contacting portion extending from the process vessel to the dust collector is cooled either wholly or partly, to a dew point of the gas or below.