A method for polishing a Cu film comprises contacting a Cu film formed above a semiconductor substrate with a polishing pad attached to a turntable, and supplying a first chemical liquid which promotes the polishing of the Cu film and a second chemical liquid which contains a surfactant, to the polishing pad while the turntable being rotated, thereby polishing the Cu film, while monitoring at least one of a table current of the turntable and a surface temperature of the polishing pad to detect a change in at least one of the table current of the turntable and the surface temperature of the polishing pad. The supply of the second chemical liquid is controlled in conformity with the change.