PURPOSE: To carry out stable abrasive finishing of end face with high accuracy by forming the top face of a rotary polishing disk into a concave or convex conical surface or a concavely curved surface, and making a ferrule carry out a circular orbital motion to carry out end-face polishing.

CONSTITUTION: A polishing disk 41 is rotated at a high speed, a ferrule 60 is inserted into the inserting hole 42c of the front end part 42a of a holding board 42, and the notched part 60c of a flange part 60b is engaged with an engaging pin 42f. Then, the ferrule 60 is pressed downward by means of a retainer member and its end face 60a is brought in pressure contact with a concave conical surface 41a which is inclined at θ°, of the rotary polishing disk 41, at a suitable pressing force. Next, the ferrule holding board 42 is made carry out a circular orbital motion by means of a circular orbit mechanism, making the ferrule 60 revolve at a low speed coaxially around the rotary shaft F of the polishing disk 41, to polish its end face 60a. Thus, by setting a ferrule merely one time in a holding board, abrasive finishing of its end face a convex conical surface or a curved surface can be stably carried out with high accuracy.