A connector that is connected to a cable, said cable comprising: at least one high-speed signal transmission line covered by a shield layer (21, 21A) and a drain line, said drain line being disposed along its respective high-speed signal transmission line and being connected to the shield layer (21, 21A), said at least one high-speed signal transmission line, shield layer (21, 21A) and drain line being enclosed with a cable braided shield, wherein the connector comprises: an inner housing (13, 47) made of an insulating material; at least one signal contact that is accommodated in the inner housing (13, 47) and respectively connected to the at least one high-speed signal transmission line exposed from the shield layer (21, 21A); a signal ground contact (35, 43) that is accommodated in the inner housing (13, 47) and connected to the drain line; a connector shield portion (32, 36, 44) that is connected to the signal ground contact (35, 43) and surrounds on at least three sides an exposed portion of the at least one high-speed signal transmission line exposed from the shield layer in the inner housing, said connector shield portion (32, 36, 44) forming hence a shield portion with three faces inside the inner housing (13, 47); and a frame ground shell that covers the inner housing (13, 47) and is connected to the cable braided shield. at least one high-speed signal transmission line covered by a shield layer (21, 21A) and a drain line, said drain line being disposed along its respective high-speed signal transmission line and being connected to the shield layer (21, 21A), said at least one high-speed signal transmission line, shield layer (21, 21A) and drain line being enclosed with a cable braided shield, wherein the connector comprises: an inner housing (13, 47) made of an insulating material; at least one signal contact that is accommodated in the inner housing (13, 47) and respectively connected to the at least one high-speed signal transmission line exposed from the shield layer (21, 21A); a signal ground contact (35, 43) that is accommodated in the inner housing (13, 47) and connected to the drain line; a connector shield portion (32, 36, 44) that is connected to the signal ground contact (35, 43) and surrounds on at least three sides an exposed portion of the at least one high-speed signal transmission line exposed from the shield layer in the inner housing, said connector shield portion (32, 36, 44) forming hence a shield portion with three faces inside the inner housing (13, 47); and a frame ground shell that covers the inner housing (13, 47) and is connected to the cable braided shield. an inner housing (13, 47) made of an insulating material; at least one signal contact that is accommodated in the inner housing (13, 47) and respectively connected to the at least one high-speed signal transmission line exposed from the shield layer (21, 21A); a signal ground contact (35, 43) that is accommodated in the inner housing (13, 47) and connected to the drain line; a connector shield portion (32, 36, 44) that is connected to the signal ground contact (35, 43) and surrounds on at least three sides an exposed portion of the at least one high-speed signal transmission line exposed from the shield layer in the inner housing, said connector shield portion (32, 36, 44) forming hence a shield portion with three faces inside the inner housing (13, 47); and a frame ground shell that covers the inner housing (13, 47) and is connected to the cable braided shield.