A composite heating apparatus provided with means for both high frequency dielectric heating and resistance heating. At the start of cooking, all the input power is supplied to the heater to accelerate the rise of the temperature in the heating chamber, and the power input to the heater is automatically controlled when the temperature in the heating chamber reaches a predetermined temperature to maintain the temperature in the heating chamber constant. At the same time, the high frequency generator is operated at comparatively low output. This makes possible the simultaneous cooking by dielectric and resistance heating even in areas not favored with a satisfactory power supply situation on the one hand and, on the other hand, is expected to contribute to energy saving in areas favored with a satisfactory power supply condition.