A fuel supply for an internal combustion engine includes an improved construction for inhibiting vapor from appearing in the fuel supplied to the engine's combustion chamber(s). A fuel injector, as one of fuel supply devices, is provided for supplying fuel to the combustion chamber of the engine. There are a first and second fuel reservoirs. The first fuel reservoir stores fuel and delivers it to the second fuel reservoir through a first fuel supply conduit, while the second fuel reservoir temporarily store the fuel and delivers it to the fuel injector through a second fuel supply conduit. The excess fuel is returned to the second fuel reservoir from the fuel injector through a fuel return conduit. The fuel supply includes a fuel cooling device for cooling the fuel passing through at least one of the conduits. The construction of the fuel supply and the fuel cooling device permits them to be located with the tight confines between the engine and a protective enclosure (e.g., a cowling of an outboard motor).