A vehicle-body structure of a vehicle includes a first frame forming a closed cross-section portion, a reinforcing member disposed in the closed cross-section portion and connected to the first frame, and another vehicle-body member connected to an outer surface of the first frame. A connection portion of the first frame and the reinforcing member includes a rigid joint portion where the first frame and the reinforcing member are joined, and a flexible joint portion where the first frame and the reinforcing member are joined, with a damper member being disposed therebetween. The other vehicle-body member is connected to the first frame in a manner such that at least a part of the other vehicle-body member overlaps the flexible joint portion in a thickness direction of the first frame, and has a high rigidity portion that enhances rigidity at the part that overlaps the flexible joint portion.