An object of the invention is to improve the motorcycle radiator arranging construction with a view to improving the external appearance characteristic of a motorcycle. In a motorcycle having a water-cooled engine 12 installed thereon, a radiator 75 is arranged erect in a space 87 defined between the engine 12 and a rear wheel 16 in such a manner that a front surface 75a thereof is directed in a longitudinal direction of the vehicle and is supported on a body frame 11, whereby the radiator 75 is made difficult to see from the outside compared with a case where the radiator is arranged at the front of the body frame to thereby make conspicuous, for example, the design of the engine.