A gas-insulated substation having an enclosure filled with dielectric gas under pressure, comprising one electrical conductor (1) designed to be live that is of longitudinal axis (X) and placed inside the enclosure (6), and two grading shields (10, 12) surrounding in part the conductor (1), at least one of the grading shields (10) comprising a hollow electrically conductive body (14) of longitudinal axis that is substantially coaxial with the axis of the casing (6), said body (14) comprising an annular depression (22) in its outer surface and orifices (26) passing through said body (14) made in a bottom of said annular depression. Said orifices (26) ensure that the dielectric gas flows between an inside zone and a zone that is outside the grading shield (10) by convection exchange.