To provide a stack gas desulfurizing method and a stack gas desulfurizer used therefor by which fine dust which has been difficult to remove is effectively collected and removed only by adding a simple equipment without consuming a large amt. of energy, scaling-up the equipment or complicating the equipment.

The exhaust gas freed from dust by a dust collector 2 is cooled in a heat exchanger 3, then humidified, cooled and brought into contact with a liq. alkaline absorbent in a reaction vessel 20 to absorb and remove the SOX in the exhaust gas and discharged into the atmosphere. In this case, the exhaust gas is separated into the low-temp. exhaust gas to be cooled in the heat exchanger 3 and the high-temp. exhaust gas 11 bypassing the heat exchanger, the low-temp. exhaust gas is humidified and cooled in a first cooling tower 10 to form a low-temp. steam-saturated exhaust gas, the high-temp. exhaust gas is humidified and cooled in a second cooling tower 12 to form a high-temp. steam-saturated exhaust gas, both exhaust gases are mixed to generate a mist, and the mixture is introduced into the reaction vessel 20.