A vehicle-body structure for suppressing deformation of a lift gate opening is provided. Embodiments include a vehicle having a rear annular framework formed from a cross member, side braces, connecting members, and a rear header; a rear suspension on lower surfaces of side pillars in the same position as the cross member in a vehicle front-rear direction; and wheel well inner portions on the vehicle rear side with respect to the cross member, each having an upper end having a damper supporting portion for mounting a suspension damper. The side braces each connect a place near the cross member and a place near the damper supporting portion to each other in a vehicle up-down direction; and the connecting members each connect a place near each end portion of the rear header in a vehicle width direction and the place near the damper supporting portion to each other.