A rotating preparatory abrasion roller finely abrades the surface of a web, which is to be a support of a lithographic plate, in preparatory abrading prior to main graining for graining the surface of the web. The preparatory abrasion roller, which is arranged against one surface of the running web, is pressed into an interval between a pair of supporting rollers, which are arranged at a predetermined interval against the other surface of the web. Consequently, the surface of the web is finely abraded in contact with a relatively large area on the surface of the preparatory abrasion roller in the state wherein the web laps with the part of the preparatory abrasion roller.