To polish a work object surface as a mirror surface having small surface roughness without impairing shape accuracy of the work object surface worked in a highly accurate aspheric shape by machine work such as NC grinding work.

In an aspheric surface polishing tool, plurally dividedly constituted polishing pellet pieces 25 are arranged in an annular ring shape on a sticking pan 23 by interposing an elastic member 24, the respective polishing pellet pieces 25 are constituted so as to be freely rotatable by following rotation of a workpiece in a state of being brought into pressure contact with a work object surface, and are constituted so as to freely swing to slide on the work object surface via the sticking pan 23.