A terry cloth cover for a clamp on sponge mop is provided. The cover is tubular and closed at one end with the other end being open and provided with Velcro patches in order that it may be fitted over the sponge and closed. Holes are provided to fit over the conventional studs that are used in the sponge for fitting on the mop clamp on base. The loops or pile on the terry cloth enable the mop to reach depressions in embossed floor tile surfaces for enhanced cleaning.