In a motorcycle provided with a water-cooling type engine mounted to a lower portion of a motorcycle body, a radiator unit is arranged in front of the engine. The radiator unit is disposed so as to cover the front wheel and a cylinder head of the cylinder assembly from a front side thereof and is connected to the engine through a hose, the radiator unit has a vertically rectangular shape in an elevational section and is mounted to the motorcycle body through a rotational shaft extending vertically on lateral one side of the radiator unit in a traveling direction of the motorcycle, so that another one side one thereof is swung forward around the rotational shaft.