There are disclosed a polishing method and a polishing device in which cleaning of a glass substrate surface can be achieved to a high level. A glass substrate (MD substrate 1) in the shape of a circular disc having a circular hole in a center portion is polished with an abrasive liquid 50 containing free abrasive grains being supplied, and an inner peripheral end surface of the glass substrate is polished using the abrasive liquid containing the free abrasive grains by rotating a rotary brush 4 or a polishing pad in contact with the inner peripheral end surface.