A wafer polishing apparatus capable of maintaining a drive ring in a flat state and a wafer polishing method are provided.In the wafer polishing apparatus and method according to an embodiment, when the head assembly moves to the initial descending position by the wafer elevation unit, the shape of the drive ring inside the head assembly may be measured by using the sensor, and thus the polishing process may be performed in the state where the descending position of the head assembly is automatically adjusted by using the head auxiliary elevation unit to maintain the drive ring in the flat state.Therefore, since the wafer polishing process is performed in the state the balance of the wafer mounting part is automatically adjusted by using the drive ring, the polishing quality of the wafer may be uniformly maintained, and also the polishing performance may be improved.