Provided is a fuel supply device which supplies a gaseous fuel by evaporating a liquid fuel. The fuel supply device is provided with an evaporator which includes a heater that heats the liquid fuel, and an electric heater which adjusts the temperature of the heater. The heater has a heat transfer surface that supplies heat to the liquid fuel. The temperature of the heater is changed on the basis of a difference between the temperature of the heat transfer surface of the heater and the boiling point of the fuel in the evaporator, and a heat flux on the heat transfer surface is adjusted.