The present invention relates to a method and an apparatus for polishing a surface of a substrate having a film whose thickness varies along a circumferential direction of the substrate. The polishing method includes: obtaining a film-thickness distribution in a circumferential direction of a substrate (W); determining a first area having a maximum or minimum film thickness based on the film-thickness distribution; rotating a polishing table (3) holding a polishing pad (2); pressing a surface of the substrate (W) against the polishing pad (2) while rotating the substrate by a polishing head (1); and polishing the first area at a removal rate different from that of a second area in the surface of the substrate (W).