A glass run structure for a vehicle door, in which a glass run is formed from a glass run body with a substantially U-shaped cross section, as well as a bottom and sidewalls provided on both sides of the bottom; and a hollow inner lip and an outer lip extending inward from an open end of the glass run body. The sidewall is formed from a steel member with an L-shaped cross section. The glass run is mounted to a sash provided in a window frame of a door panel above a belt line; while in a lower end portion below the belt line, the glass run is fixed by welding to an attachment portion of a bracket that is held by a bolt to the door panel.