A method and an apparatus for forming a hemispherical convex mirror surface on the end of a ferrule or optical fiber connector efficiently and accurately. The apparatus has a grinding wheel having a concave work surface, a tool for correcting the shape of the work surface, a stage for bringing the tool into contact with the wheel, a mechanism for causing the end of the ferrule to contact the work surface, and a mechanism for displacing the axis of the ferrule from the center of the curvature of the arcuate section of the work surface. After the axis of the ferrule has been displaced from the center of the curvature, the ferrule is caused to contact the work surface and roughly ground thereby. Subsequently, after the ferrule axis has been brought into alignment with the center of curvature, the ferrule is sequentially finished from the tip to a preselected point thereof.