A flue gas desulfurization apparatus includes at least one activated carbon fiber board 20 provided in a catalyst unit 6, the board being formed by alternatingly juxtaposing one or more plate-like activated carbon fiber sheets and one or more corrugated activated carbon fiber sheets so as to provide vertically extending conduits, wherein water for producing sulfuric acid is supplied, through a capillary phenomenon, to the activated carbon fiber board 20 provided in the catalyst unit 6. The flue gas desulfurization apparatus attains removal of sulfur oxides (SO.sub.x) by adding a minimum required amount of water to the activated carbon fiber board 20 so as to attain uniform water distribution and can reduce the amount of water required for removing sulfur oxides (SO.sub.x).