A lower vehicle-body structure of a vehicle, the lower vehicle-body structure comprising: left and right rear frames forming a closed cross section extending substantially in a vehicle longitudinal direction; and arm front-end supporting portions (20, 20A) that are on lower portions of the rear frames and are for supporting left and right trailing arm front ends of a rear suspension, the arm front-end supporting portions (20, 20A) each having a squared U-shape portion (21, 21A) including an outer wall portion on an outer side in a vehicle width direction, an inner wall portion (23, 23A) on an inner side in the vehicle width direction, and a front wall portion (24, 24A) with a rear side being open when viewed from bottom, each of the arm front-end supporting portions (20, 20A) including: an extending outer wall portion extending from the outer wall portion to a place in front of the front wall portion (24, 24A), the outer wall portion and the extending outer wall portion being formed by a side sill inner portion joined to each of the rear frames; and an extending inner wall portion (26, 40) extending from the inner wall portion (23, 23A) to a place in front of the front wall portion (24, 24A), the extending inner wall portion (26, 40) being joined to each of the rear frames, wherein the front wall portion forms a surface extending in the vehicle width direction at a place below a lower wall portion of the rear side frame and a joining flange portion is integrally formed in a bent manner on the upper end of the surface of the front wall portion, wherein the joining flange portion extends to the front side of the vehicle so as to be joined to the lower portion of the rear side frame. left and right rear frames forming a closed cross section extending substantially in a vehicle longitudinal direction; and arm front-end supporting portions (20, 20A) that are on lower portions of the rear frames and are for supporting left and right trailing arm front ends of a rear suspension, the arm front-end supporting portions (20, 20A) each having a squared U-shape portion (21, 21A) including an outer wall portion on an outer side in a vehicle width direction, an inner wall portion (23, 23A) on an inner side in the vehicle width direction, and a front wall portion (24, 24A) with a rear side being open when viewed from bottom, each of the arm front-end supporting portions (20, 20A) including: an extending outer wall portion extending from the outer wall portion to a place in front of the front wall portion (24, 24A), the outer wall portion and the extending outer wall portion being formed by a side sill inner portion joined to each of the rear frames; and an extending inner wall portion (26, 40) extending from the inner wall portion (23, 23A) to a place in front of the front wall portion (24, 24A), the extending inner wall portion (26, 40) being joined to each of the rear frames, wherein the front wall portion forms a surface extending in the vehicle width direction at a place below a lower wall portion of the rear side frame and a joining flange portion is integrally formed in a bent manner on the upper end of the surface of the front wall portion, wherein the joining flange portion extends to the front side of the vehicle so as to be joined to the lower portion of the rear side frame. an extending outer wall portion extending from the outer wall portion to a place in front of the front wall portion (24, 24A), the outer wall portion and the extending outer wall portion being formed by a side sill inner portion joined to each of the rear frames; and an extending inner wall portion (26, 40) extending from the inner wall portion (23, 23A) to a place in front of the front wall portion (24, 24A), the extending inner wall portion (26, 40) being joined to each of the rear frames, wherein the front wall portion forms a surface extending in the vehicle width direction at a place below a lower wall portion of the rear side frame and a joining flange portion is integrally formed in a bent manner on the upper end of the surface of the front wall portion, wherein the joining flange portion extends to the front side of the vehicle so as to be joined to the lower portion of the rear side frame.