Exhaust (Flue) gas of boiler is introduced through gas inlet part (port) (2) of flue-gas desulfurization apparatus (system), and absorbent liquid sprayed from spray nozzle (5) of absorbent liquid spray section (4) is trapped (stored) in liquid trapping (recirculation tank) section (7). There, agitation is performed by means of propeller (11) of oxidation agitator (8) to thereby oxidize SO.sub.2 absorbed from the exhaust (flue) gas into gypsum. In the liquid trapping section (7), oxidation air is fed from posterior air pipe (10) and anterior air pipe (13) behind and ahead of liquid propulsion (to the rear and front of a liquid discharge) by the propeller (11). Thus, even when the amount of oxidation air must be increased in accordance with an increase of boiler load, the oxidation efficiency can be enhanced without increasing of the number of agitators. Accordingly, there can be provided a wet flue-gas desulfurization apparatus (system) and method with which even when the amount of oxidation air fed to the liquid trapping section is increased, highly efficient oxidation can be performed without increasing the number of agitators installed and the operating cost.