A bumper cross member for a motor vehicle includes an insert of fiber-reinforced composite material and reinforcing structures molded onto the insert. A first groove is formed onto the insert, and the reinforcing structures include ribs formed in the first groove. The ribs extend inclined in relation to a longitudinal direction of the groove from one lateral wall of the groove to the other. The insert is further formed into a second groove, which are open toward opposing sides of the insert. The first and second grooves share a lateral wall. An outer bumper skin is supported by the bumper cross member.