A high frequency heating apparatus equipped with the oven hood comprises a heating chamber, a power supply apparatus for controlling high frequency output power by way of a semiconductor element, ventilation, and illumination for illuminating an object to be heated by another heat-cooking apparatus. Since the high frequency output power is controlled in such a manner that an optimum heating output power is applied in a linear manner for a proper time period, the heating output power can be controlled in the linear manner and the high frequency heating apparatus can be largely reduced in weight. As a result, the highest-speed heat-cooking operation by receiving the maximum high frequency output power can be realized, and the optimum cooking performance can be realized. Both the installation performance of the appliance to the mounting wall plane and the safety performance achieved by stably fixing the appliance can also be largely improved.