A glass run capable of being readily attached to corner parts of a door frame of a door of a motor vehicle such that an end edge of a corner cover of the glass run can be securely engaged with an end of a corner piece. A corner cover adapted to cover a vehicle-exterior surface of the corner piece like an arcuate configuration is formed in a corner section of the glass run. An arcuate end edge of the corner cover defines a corner cover lip for contacting an end of the corner piece, and a corner cover engaging wall is formed in the corner cover so as to protrude inwardly from a vehicle-interior surface of the corner cover lip. The corner cover engaging wall and the corner cover lip define an engaging groove, and a plurality of corner cover inclination ribs are formed so as to respectively have an inclined surface connecting the corner cover engaging wall and the vehicle-interior surface of the corner cover lip.