A polishing apparatus is used for polishing a substrate such as a semiconductor wafer to a flat mirror finish. The polishing apparatus includes a polishing table having a polishing surface, a polishing head having at least one elastic membrane configured to form a plurality of pressure chambers for being supplied with a pressurized fluid, and a controller configured to control supply of the pressurized fluid to the pressure chambers. The controller controls supply of the pressurized fluid so that the pressurized fluid is supplied first to the pressure chamber located at a central portion of the substrate when the substrate is brought into contact with the polishing surface, and then the pressurized fluid is supplied to the pressure chamber located at a radially outer side of the pressure chamber located at the central portion of the substrate.