To provide a wafer polisher capable of uniformly polishing the whole surface of a wafer by preventing excessive polishing for the outer peripheral edge of the wafer.

In this polisher, a retainer ring 28 is supported on a head main body to be freely rotated around an axis P2 eccentric from an axis P1 of rotation of a carrier 24. The retainer ring 28 is also rotatably supported on the head main body 22 so that the axis P2 thereof is positioned on the downstream side in the rotating direction of a polishing pad 16 to the axis P1 of rotation of the carrier 24. Thus, the inner peripheral edge 28A of the retainer ring 28 positioned on the downstream side in the rotating direction of the polishing pad 16 is kept apart from the outer peripheral edge 50A of the wafer 50, and a raised part 16C caused on the downstream side in the rotating direction of the polishing pad 16 is caused between the inner peripheral edge 28 of the separated retainer ring 28 and the outer peripheral part 50A of the wafer 50.