A polishing apparatus is used for polishing a workpiece such as a semiconductor wafer to a flat mirror finish. The polishing apparatus includes a polishing section for polishing a surface of a workpiece, a cleaning section for cleaning the workpiece which has been polished, a first liquid leakage sensor provided in the polishing section for detecting a liquid leakage which occurs in the polishing section, and a second liquid leakage sensor provided in the cleaning section for detecting a liquid leakage which occurs in the cleaning section. The polishing apparatus further includes a controlling device for stopping the supply of liquid to the polishing section or the cleaning section in which the liquid leakage occurs when either one of the first and second liquid leakage sensors detects the liquid leakage.