This wafer polishing apparatus includes: a polishing plate having a polishing pad; a carrier plate which is placed facing the polishing pad and which slides and presses wafers against the polishing pad, while rotating in a state of holding the wafers; and an abrasive slurry supply device, wherein the abrasive slurry supply device is able to supply different abrasive slurries, each of the abrasive slurries contains abrasives of which the average grain size is different from those contained in the other abrasive slurries. This method for polishing wafers includes: while supplying an abrasive slurry to a surface of a polishing pad, sliding and pressing wafers against the polishing pad, wherein different abrasive slurries are supplied to the surface of the polishing pad, and each of the abrasive slurries contains abrasives of which the average grain size is different from those contained in the other abrasive slurries.