PURPOSE: To carry out the dry desulfurization and the cooling of an exhaust gas at a low cost in a simple process, by removing sulfur oxide in the exhaust gas by reacting the same in the presence of moisture and a calcium compound powder.

CONSTITUTION: On the way of a duct 1 for sending an exhaust gas containing sulfur oxide from a combustion furnace, a water spray pipe 2 spraying water or steam toward the exhaust gas and a powder supply pipe 3 for supplying a calcium compound powder such as a calcium carbonate powder are provided so as to open one ends at an almost same position. By this mechanism, carbon dioxide and sulfur oxide in the exhaust gas are desulfurized and cooled and collected and removed in cyclones 5, 6 through an exhaust fan 4. As is apparent from the above description, the desulfurization and the cooling of the exhaust gas is carried out at a low cost by a simple treating method.