A mirror-finishing method embodying this invention, with which the above and other objects can be accomplished, may be characterized as comprising the step of supplying a solution containing hydroxyl groups on a target surface to be polished of a glass substrate while simultaneously pressing onto this target surface an elastic sponge material having abrading particles affixed therein and a plurality of indentations on a polishing surface thereof, and causing the substrate and the sponge material to move with respect to each other.