Abstract: Disclosed are method and apparatus for generating compound plasma and electro-thermal cooking apparatus using the compound plasma. An electro-thermal cooking apparatus has an evaporator for generating water vapor by heating water therein with electric energy, a blast nozzle for blasting the water vapor supplied from the evaporator, and an electric discharge means, installed in an insulating body around the blast nozzle, for making the water vapor electrically discharged by applying strong energy to the water vapor blasted from the blast nozzle so as to convert the water vapor into compound plasma of hydrogen plasma and oxygen plasma. The compound plasma is used as an energy transfer medium for a cooking utensil. According to the present invention, efficiency of heat transfer is improved because the compound plasma of high temperature of which energy density is relatively high is used, although it employs electrically heating method. The heating time can also be reduced even with a downsized device.