The present invention relates to a polishing apparatus and a polishing method for polishing a substrate, such as a semiconductor wafer, to planarize the substrate. The polishing apparatus according to the present invention includes a polishing table (10) having a polishing surface, a top ring (14) configured to press the substrate against the polishing table by applying pressing forces independently to first plural zones on the substrate, a sensor (50) configured to detect a state of the film at plural measuring points, a monitoring device (53) configured to produce monitoring signals with respect to second plural zones on the substrate, respectively, a storage device configured to store plural reference signals each indicating a relationship between reference values of each monitoring signal and polishing times, and a controller configured to operate the pressing forces against the first plural zones such that the monitoring signals, corresponding respectively to the second plural zones, converge on one of the plural reference signals.