A polishing apparatus includes a polishing pad for polishing a wafer and a polishing head for holding the wafer. The polishing head includes a retainer ring, a membrane sheet, and a head body. The retainer ring retains the wafer in a horizontal direction. The membrane sheet depresses the wafer to the polishing pad. The head body supports the retainer ring and the membrane sheet. The retainer ring includes a fixed retainer ring and a released retainer ring. The released retainer ring is interposed between the inner periphery of the fixed retainer ring and the periphery of the wafer to retain the wafer in the horizontal direction.