A motorcycle having an engine with a turbo-supercharger in which the engine is mounted on a body frame between front and rear wheels. A first and a second muffler are disposed on the opposite sides of the rear wheel. An exhaust pipe extending from the engine is connected to the first muffler. The supercharger has a turbine disposed in the exhaust pipe so that it is driven by exhaust gas flowing through the exhaust pipe. A waste pipe is branched from the exhaust pipe at a position upstream of the turbine and is connected to the second muffler for discharging a part of exhaust gas while bypassing the turbine. With this arrangement, layout of the exhaust system can be effected neatly to provide a good appearance as well as a good balance in weight-distribution and in banking angle of the motorcycle.