An upper vehicle-body structure for a vehicle, comprising: a roof opening-closing unit which has a cover member being capable of opening and closing a generally rectangular opening formed in a roof panel; and a vehicle-body framework member which surrounds an outer edge portion of the opening and in which corner portions (C1a, C1b) are formed in a planar view, wherein the roof opening-closing unit has a unit framework member which is in a generally rectangular shape in a planar view and in which corner portions (C2a, C2b) are formed, and portions of the unit framework member close to unit corner portions (C2a, C2b) are coupled with portions of the vehicle-body framework member close to vehicle-body corner portions (C1a, C1b), characterized in that the vehicle-body framework member includes a pair of left and right roof side rails extending in a vehicle front-rear direction, a front header coupling front end portions of the pair of roof side rails together in a vehicle width direction, and a roof reinforcement coupling rear-side intermediate portions of the pair of roof side rails together in the vehicle width direction, the unit framework member is coupled with the vehicle-body framework member via a pair of left and right front-side brackets and a pair of left and right rear-side brackets, the front-side bracket is fastened to the front header at two vehicle-body-side fastening points (h1, h2) aligned in the vehicle width direction, the front-side bracket is fastened to the unit framework member at at least two unit-side fastening points (h3, h4) aligned in the vehicle front-rear direction, one vehicle-body-side fastening point of the vehicle-body-side fastening points (h1, h2) is disposed in a close position to an extension line connecting the two unit-side fastening points (h3, h4), and a remaining vehicle-body-side fastening point of the vehicle-body-side fastening points (h1, h2) is disposed in a position on a vehicle-width-direction outer side of the extension line, and the front-side bracket has a bead extending in the vehicle front-rear direction between the two vehicle-body-side fastening points (h1, h2) and a flange portion bent in an up-down direction in a vehicle-width-direction outer side end. a roof opening-closing unit which has a cover member being capable of opening and closing a generally rectangular opening formed in a roof panel; and a vehicle-body framework member which surrounds an outer edge portion of the opening and in which corner portions (C1a, C1b) are formed in a planar view, wherein the roof opening-closing unit has a unit framework member which is in a generally rectangular shape in a planar view and in which corner portions (C2a, C2b) are formed, and portions of the unit framework member close to unit corner portions (C2a, C2b) are coupled with portions of the vehicle-body framework member close to vehicle-body corner portions (C1a, C1b), characterized in that the vehicle-body framework member includes a pair of left and right roof side rails extending in a vehicle front-rear direction, a front header coupling front end portions of the pair of roof side rails together in a vehicle width direction, and a roof reinforcement coupling rear-side intermediate portions of the pair of roof side rails together in the vehicle width direction, the unit framework member is coupled with the vehicle-body framework member via a pair of left and right front-side brackets and a pair of left and right rear-side brackets, the front-side bracket is fastened to the front header at two vehicle-body-side fastening points (h1, h2) aligned in the vehicle width direction, the front-side bracket is fastened to the unit framework member at at least two unit-side fastening points (h3, h4) aligned in the vehicle front-rear direction, one vehicle-body-side fastening point of the vehicle-body-side fastening points (h1, h2) is disposed in a close position to an extension line connecting the two unit-side fastening points (h3, h4), and a remaining vehicle-body-side fastening point of the vehicle-body-side fastening points (h1, h2) is disposed in a position on a vehicle-width-direction outer side of the extension line, and the front-side bracket has a bead extending in the vehicle front-rear direction between the two vehicle-body-side fastening points (h1, h2) and a flange portion bent in an up-down direction in a vehicle-width-direction outer side end.