A rear vehicle-body structure of a vehicle, comprising: a damper support section for a rear suspension; a first loop-shaped structure section provided to extend continuously along a lower wall part, right-and-left side wall parts, and an upper wall part of a vehicle body so as to have a loop shape in a vehicle elevational view, the first loop-shaped structure section being positioned in front or on a forward side, in a vehicle longitudinal direction, of the damper support section; and a second loop-shaped structure section provided to extend continuously along a lower wall part, right-and-left side wall parts, and an upper wall part of the vehicle body so as to have a loop shape in the vehicle elevational view, the second loop-shaped structure section being positioned behind or on a rearward side of the damper support section, in the vehicle longitudinal direction, wherein each of the first and second loop-shaped structure sections (Z1, Z2) is formed by a closed-cross section portion (24, 28, 42, 48, 81, 84, 86) where a closed-cross section is partitioned by plural members, and/or a thick plate portion having a thicker plate thickness than a vehicle-body panel, wherein the vehicle-body lower wall part of the first loop-shaped structure section includes a closed-cross section portion formed by a floor panel and a floor cross member (23, 25) joined to the floor panel, wherein each of the vehicle-body side wall parts of the first loop-shaped structure section includes a closed-cross section portion (81, 84) formed by a rear wheel house, a first brace member and a pillar which are joined to the rear wheel house, wherein the vehicle-body upper wall part of the first loop-shaped structure section includes a closed-cross section portion formed by a roof panel and a roof reinforcement joined to the roof panel, wherein the vehicle-body lower wall part of the second loop-shaped structure section includes a closed-cross section portion formed by the floor panel and a second floor cross member joined to the floor panel, characterized in that each of the vehicle-body side wall parts of the second loop-shaped structure section includes a closed-cross section portion formed by the rear wheel house, a side panel and a second brace member which is joined to the rear wheel house and the side panel, and the vehicle-body upper wall part of the second loop-shaped structure section includes a closed-cross section portion formed by the roof panel and a rear header joined to the roof panel. a damper support section for a rear suspension; a first loop-shaped structure section provided to extend continuously along a lower wall part, right-and-left side wall parts, and an upper wall part of a vehicle body so as to have a loop shape in a vehicle elevational view, the first loop-shaped structure section being positioned in front or on a forward side, in a vehicle longitudinal direction, of the damper support section; and a second loop-shaped structure section provided to extend continuously along a lower wall part, right-and-left side wall parts, and an upper wall part of the vehicle body so as to have a loop shape in the vehicle elevational view, the second loop-shaped structure section being positioned behind or on a rearward side of the damper support section, in the vehicle longitudinal direction, wherein each of the first and second loop-shaped structure sections (Z1, Z2) is formed by a closed-cross section portion (24, 28, 42, 48, 81, 84, 86) where a closed-cross section is partitioned by plural members, and/or a thick plate portion having a thicker plate thickness than a vehicle-body panel, wherein the vehicle-body lower wall part of the first loop-shaped structure section includes a closed-cross section portion formed by a floor panel and a floor cross member (23, 25) joined to the floor panel, wherein each of the vehicle-body side wall parts of the first loop-shaped structure section includes a closed-cross section portion (81, 84) formed by a rear wheel house, a first brace member and a pillar which are joined to the rear wheel house, wherein the vehicle-body upper wall part of the first loop-shaped structure section includes a closed-cross section portion formed by a roof panel and a roof reinforcement joined to the roof panel, wherein the vehicle-body lower wall part of the second loop-shaped structure section includes a closed-cross section portion formed by the floor panel and a second floor cross member joined to the floor panel, characterized in that each of the vehicle-body side wall parts of the second loop-shaped structure section includes a closed-cross section portion formed by the rear wheel house, a side panel and a second brace member which is joined to the rear wheel house and the side panel, and the vehicle-body upper wall part of the second loop-shaped structure section includes a closed-cross section portion formed by the roof panel and a rear header joined to the roof panel.