An edge section of a wafer can be polished, and at same time, a polishing surface of a polishing member can be dressed by a dresser mechanism. A polishing member has annular concave trenches, which are coaxially formed in the front surface thereof, and at least an inner surface of the concave trenches is composed of an inclined polishing surface for polishing an edge section of the wafer, and a wafer pressing mechanism presses the edge section of the wafer against the inner surfaces in at least one side of the concave trench of the polishing member, and a dresser mechanism dresses at least the inner surfaces in at least one side of the concave trench of the polishing member.