A substrate polishing apparatus includes a substrate holding mechanism having a head for holding a substrate to be polished, and a polishing mechanism including a polishing table with a polishing pad mounted thereon. The substrate held by the head is pressed against the polishing pad on the polishing table to polish the substrate by relative movement of the substrate and the polishing pad. The substrate polishing apparatus also includes a substrate transfer mechanism for delivering the substrate to be polished to the head and receiving the polished substrate. The substrate transfer mechanism includes a substrate to-be-polished receiver for receiving the substrate to be polished, and a polished substrate receiver for receiving the substrate which has been polished.