The present invention provides an apparatus and a method for polishing a substrate having a film formed thereon. The method includes: rotating a polishing table supporting a polishing pad by a table motor; pressing the substrate against the polishing pad by a top ring; obtaining a signal containing a thickness information of the film; producing from the signal a polishing index value that varies in accordance with a thickness of the film; monitoring a torque current value of the table motor and the polishing index value; and determining a polishing end point based on a point of time when the torque current value has reached a predetermined threshold value or a point of time when a predetermined distinctive point of the polishing index value has appeared, whichever comes first.