An end face polishing apparatus has a lapping board mounted to undergo rotation and revolving movement, a lapping member having a polishing surface and disposed on the lapping board for rotation and revolving movement therewith, a polishing fixture for supporting a workpiece having an end face, and a pressing member. During a polishing operation, preselected portion thereof to bring the end face of the workpiece into pressure contact with the polishing surface of the lapping member and to dispose the preselected portion at a position closer to the polishing surface than to a center of gravity of the polishing fixture to thereby polish the end face of the workpiece during rotation and revolving movement of the lapping board.