A reinforced annular bicycle rim is provided that includes a tire attachment portion and a spoke attachment portion fixedly coupled with the tire attachment portion to form an annular hollow area. A plurality of separate reinforcement members are fixedly coupled to an exterior surface of the spoke attachment portion to effectively increase the thickness of the rim at circumferentially spaced locations. Each of the reinforcement members is located exteriorly of the hollow area. Openings extend through the reinforcement members and the spoke attachment portion to couple spokes to the rim. A method of making such a rim is also provided. Preferably, the reinforcement members are welded or brazed to the spoke attachment portion, and then the openings are formed in the spoke attachment portion and the reinforcement members.