To perform simple and high-precision polishing of both the flank of the cutting edge of the tip of a drill and web thinning.

After the chisel part 22 of the central part of the blade flank of the tip of a drill 21 is centered by a centering part 15, a drill 21 is fixed at a drill chuck 8, and the chuck holder 6 of the drill chuck 8 is caused to approach a disc grinder 2 and revolved in a given angle arc around a suspending support shaft 3. The flank 28 of the cutting edge 16 of the tip of a drill 20 is brought into contact with the inner polishing surface of the staged peripheral part 25 of the disc grinder 2 and the flank 28 of the cutting edge 16 is polished. The chuck holder 6 of the drill chuck 8 is reversely revolved in a given angle arc around the support shaft 3, the chisel part 22 of the drill 21 is brought into contact with the outside polishing surface of the staged peripheral part 25 of the disc grinder 2 to effect polishing, and both the flank of the cutting edge and web thinning are polished by one chucking.