To allow the performance of one-step polishing or plural-step polishing in high throughput, and reduce the overall size as well as the occupied area of an apparatus.

A wafer polishing apparatus comprises: a first wafer holding head 26 and a second wafer holding head 27 that are placed on two platens 21 and 22, respectively; and a wafer transfer device 23 for placing a wafer between the two platens 21, 22. The two wafer-holding heads 26, 27 are moved by a first moving means 33 and a second moving means 34, respectively, between the two platens 21, 22 and the wafer transfer device 23. In addition, the wafer-holding heads 26, 27 are rotation-moved 180 degrees, from one platen 21 or 22 to the other platen 22 or 21, by a rotating/moving means 35 that supports the two moving means 33, 34, thus two-step polishing being implemented.