A substrate polishing apparatus for polishing a polishing surface of a substrate has a film thickness monitoring device for monitoring a state of a film thickness of a thin film on the polishing surface of the substrate during polishing. The apparatus includes a table, a polishing member fixed on a surface of the table, a substrate support member for pressing the substrate onto the polishing member, an optical system composed of an optical fiber for irradiating the polishing surface of the substrate with a light of irradiation and an optical fiber for receiving a reflected light reflected on the polishing surface of the substrate, an analysis-processing system for processing an analysis of the reflected light received with the optical system, and the film-thickness monitoring device. The table is provided with a liquid-feeding opening for feeding a translucent liquid into a through-hole disposed in the polishing member.