A bumper-reinforcing system (1) intended for a motor vehicle includes: a bumper beam (2) with a single-piece elongated profile with a closed cross section and including a center zone (21) extending at least over part of the entire width of the bumper beam and an end zone (22) at each extremity of the bumper beam, two bumper fasteners (3) connected to the rear side of the bumper beam (2) at the intersection between the center zone (21) and the end zone (22) of the bumper beam (2), two reinforcing tubes (4) connected by their first end to the rear side of the end zone (22) of the bumper beam (2), extending from the bumper beam (2) so as to form an angle α below 45° with the vertical plane of symmetry of the bumper beam and suited to be connected by their other end on the front rail of the vehicle for which the bumper-reinforcing system (1) is provided, and two covers (5) with a single-piece elongated profile with an open cross section, in contact with the rear side of the end zone (22) of the bumper beam (2) and extending at least from the first end of one of the reinforcing tubes (4) to one of the bumper fasteners (3).