A vehicle having a side cover capable of sending a sufficient amount of cooling air to a radiator even without a front cover or cowling. Side covers are disposed on both right and left side surfaces for covering a radiator. An air admission portion for drawing in a cooling air for cooling the radiator is provided in each of the side covers. A main step is disposed outside of each of the air admission portions with a footpeg portion provided on a top surface thereof and a step portion projecting upwardly at a front end portion thereof. The step portion is substantially at the same position in the fore-aft direction of the vehicle as a front end of the air admission portion. The footpeg surfaces is located near a rear portion of a front wheel with the main step structure ensuring an even more comfortable and easy riding position.