A liquid fuel burner for burning liquid fuel in the form of a gaseous mixture with air. The liquid fuel burner has a porous member provided at least with a fuel receiving section for receiving the liquid fuel supplied to the burner and a fuel evaporation section from which the liquid fuel is evaporated. An air supplying device is provided for forcibly supplying air to the fuel evaporation section. The rate of air supply is varied by means of a damper or like means. Heating means are provided for maintaining the fuel evaporation section at a substantially constant temperature. The rate of burning is varied while maintaining the air-fuel ratio of the mixture substantially constant, because the rate of evaporation of the fuel is almost in proportion to the rate of supply of air to the fuel evaporation section. The heating means facilitates the evaporation of the fuel and permits a rapid rise and stabilization of burning after ignition.