An electrochemical mechanical polishing apparatus is for use in polishing of a conductive material (e.g., metal) on a surface of a substrate by combination of electrochemical action and mechanical action. This apparatus includes a polishing table having divided electrodes and adapted to hold a polishing pad having a polishing surface, a polishing head adapted to hold a workpiece having a conductive film and to press the workpiece against the polishing surface, a second electrode for supplying an electric current to the conductive film, an electrolytic-solution supply section for supplying an electrolytic solution to the polishing surface, a detecting section adapted to detect a signal corresponding to a thickness of the conductive film, a variable resistance unit having the same number of variable resistors as the number of divided electrodes, a moving mechanism for providing relative movement between the workpiece and the polishing surface, and a control section adapted to control each of the variable resistors based on the signal from the detecting section.