A process of purifying the gypsum slurry end product produced by a flue gas desulfurization process which incorporates fine solids separation/classifying, dewatering, mixing, and filtering to both achieve a useful gypsum product and to recycle as much process water as possible to the flue gas desulfurization process. This purification process separates the incoming gypsum slurry into a fine solids stream containing a disproportionate amount of impurities therein that are concentrated and subsequently disposed of and a coarse solids stream containing a large amount of gypsum therein from which a usable gypsum product is recovered.