A polishing apparatus has a polishing table (18) having a polishing surface (40) and a top ring (20) for pressing a substrate against the polishing surface (40) while independently controlling pressing forces applied to a plurality of areas (C1-C4) on the substrate. The polishing apparatus has a sensor (52) for monitoring substrate conditions of a plurality of measurement points on the substrate, a monitor unit (53) for performing a predetermined arithmetic process on a signal from the sensor (52) to generate a monitor signal, and a controller (54) for comparing the monitor signal of the measurement points with the reference signal and controlling the pressing forces of the top ring (20) so that the monitor signal of the measurement point converges on the reference signal.