The present invention discloses a method and an apparatus for flue gas desulfurization and sulfuric acid production. The method comprises that (1) flue gas is subjected to heat exchange through a sulfuric acid storage tank, and then the obtained flue gas enters a dust removing quenching tower and is subjected to primary dust removing cooling; (2) the cooled flue gas enters a desulfurization tower and sequentially passes through a deep dust removing unit, a desulfurization unit and a water washing unit from bottom to top; (3) in the water washing unit, the SOx in the flue gas is absorbed with fresh water, the liquid phase overflows and sequentially passes through the desulfurization unit and the deep dust removing unit, the obtained liquid phase enters the dust removing quenching tower to obtain a rich absorption liquid, solid-liquid separation is performed, and the gas phase is discharged in atmosphere after defogging; and (4) the rich absorption liquid being subjected to solid waste separation is discharged into an oxidation tank, the liquid phase enters a regeneration tower, the Fe<3+> / Fe<2+> in the liquid phase is removed, and the obtained liquid phase enters the sulfuric acid storage tank in the form of dilute sulfuric acid. With the method and the apparatus of the present invention, the SO2 in the flue gas can be absorbed and concentrated, and can be oxidized into the sulfuric acid so as to produce the high concentration sulfuric acid, the purified flue gas can meet the national or local relevant standard requirements, and the method and the apparatus are suitable for the recovery treatment of flue gas containing various concentrations of sulfur dioxide.