A sludge drying apparatus includes a waste fluid bath for storing a waste fluid containing a sludge, an extracting unit for extracting the sludge from the waste fluid stored in the waste fluid bath, a transfer belt for transferring the sludge extracted by the extracting unit, a drying unit for drying the sludge to be transferred by the transfer belt, and a recovering unit for recovering the sludge transferred by the transfer belt and dried by the drying unit. The recovering unit includes a roll brush provided adjacent to the air outlet so as to horizontally extend in the direction perpendicular to the direction of extension of the transfer belt, and a recovery box for recovering the sludge separated from the transfer belt by the roll brush.