A rear vehicle-body structure of a vehicle comprises a storage compartment for storing an openable roof and a back window portion, a deck cover provided to cover over the storage compartment, the deck cover comprising a pair of right-and-left cover side wall portions which are provided to be spaced apart from each other in a vehicle width direction and stand upward and a header portion which is provided to interconnect respective upper ends of the cover side wall portions at a position close to, in a vehicle longitudinal direction, the roof, a cover opening/closing mechanism provided to move the deck cover upward, and a pair of right-and-left front-lower regulation structures provided to regulate positions of respective lower portions of the cover side wall portions relative to the vehicle body.