The present invention provides a precise polishing apparatus and method in which a polished body is polished by rotating a polishing pad having a diameter greater than that of the polished body while urging the polishing pad against the polished body in conditions that a center of the polished body is deviated from a rotation axis of the polishing pad and that the polishing pad is contacted with the entire polished surface of the polished body. The polished body may be a semi-conductor wafer.