A brake support structure for effectively utilizes a space is disposed so as to be hardly visible in appearance. In addition, the brake support structure protects the pipes. A brake support structure includes a vehicle frame having rear frames extending from main frames with a swing arm having a front end pivotally supported on the rear frames and a rear end for rotatably supporting a rear wheel. Brake pipes are connected to a brake caliper for braking the rear wheel. An upper cross member interconnects the rear frames and is disposed near the swing arm. The brake pipes extend between the upper cross member and the swing arm.