A radiator structure includes a radiator body having a core composed of radiating fins and cooling water passing tubes alternately laminated and a bracket disposed at one end of the core. The bracket includes an extension portion disposed at a vehicle widthwise inner end of the core and extending along a vehicle front-rear direction. The extension portion has a fixing portion on a leading end thereof, the fixing portion being fixed to a mounting portion of a body frame. An indentation is provided in a portion of an opposed sidewall where a front end of the core and the opposed sidewall of the bracket overlap each other when the vehicle is viewed from the side and which overlaps the fixing portion at least in the vehicle front-rear direction. The indentation is formed by bending the opposed sidewall in a direction away from the front end.