A polishing method and apparatus can concurrently establish a stable removal rate, a small step height reduction rate, and reduction of detects on the polished surface for various kinds of polished subjects, while providing less environmental problems and requiring less processing costs. The method for polishing a surface of a semiconductor device wafer comprises first polishing a surface of the semiconductor wafer by a first fixed abrasive polishing method; and finish polishing the polished surface of the semiconductor wafer by a second fixed abrasive polishing method different from the first fixed abrasive polishing method.