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