In a wet lime desulfurization of exhaust gases containing SO.sub.2 and fly ash, a method and apparatus for treating absorbent solution slurry-containing fly ash includes diverting at least a part of the absorbent solution slurry containing fly ash particles, separating the diverted absorbent solution slurry by centrifugal separation into the solid gypsum component and a liquid component of a suspension containing fine fly ash particles, adjusting the pH value of the suspension containing fine fly ash particles remaining in a filtrate to 6 to 9 by adding an alkali, supplying the pH adjusted suspension to a thickener, removing concentrated sludge from the thickener, passing overflow H.sub.2 O from the thickener to a limestone slurry tank, and passing slurry from the limestone slurry tank to the absorbent solution slurry as make-up feed. Ill effects caused by fly ash and HF in exhaust gases are avoided, the activity of CaCo.sub.3 in the absorbent slurry is maintained, and highly pure gypsum is recovered.