A polishing method which can acquire an actual position of a film-thickness measurement point, and can therefore apply an optimum polishing pressure to a substrate such as a wafer is disclosed. The method includes: causing a substrate detection sensor to generate substrate detection signals in a preset cycle and causing a film-thickness sensor to generate a film-thickness signal at a predetermined measurement point during polishing of the substrate while the substrate detection sensor and the film-thickness sensor are moving across the surface of the substrate; calculating an angle of eccentricity of a center of the substrate relative to a center of the polishing head from the number of substrate detection signals; correcting a position of the predetermined measurement point based on the angle of eccentricity; and controlling polishing pressure at which the polishing head presses the substrate based on the film-thickness signal and the corrected position of the predetermined measurement point.