A glass run for use in a motor vehicle includes an outside wall, an inside wall and a bottom wall and has a generally U-shaped cross-section. An outside seal lip and an inside seal lip respectively project from open ends of the outside wall and the inside wall to extend into an interior of the glass run. An outside cover lip and an inside cover lip respectively project from the open ends of the outside wall and the inside wall for covering an outside end and an inside end of the door frame. And a corner part of the glass run, which is adapted to be attached to a corner of the door frame, has a lip extension along a projecting end of the outside cover lip for covering a joint between an upper frame and a vertical frame of the door frame.