To accommodate any variation in curvature and smooth ripples in polishing aspheric surfaces with large variations in curvature by maintaining constant polishing pressure.

A plurality of small tool plates 10 are interconnected at a hinge portion 12 so that their proximal portions can hinge relative to each other, and are provided with sheetlike abrasives 11 affixed thereto, to form small polishing tools. Each small polishing tool is removably supported on a shaft 5 via a rubber member 7 fixed on the top surface of the tool plate 10. A plurality of such shafts 5 are connected to a shaft 2 mounted on a polishing device, via vertically movable parallel leaf springs 4. The obtained polishing tool can follow any variation in the curvature of a workpiece 15 but eliminate selected ripples that it does not follow, and can provide constant polishing pressure despite of irregularities, whose influence is removed by the parallel leaf springs 4, to thereby enable high-precision machining.