In an electromagnetic induction heating apparatus, a cooking vessel made of a nonmagnetic metal, which has conventionally been incapable of magnetic inducting heating, is provided adjacent a heating coil which applies an alternating field with a high-frequency of at least 50 kHz. An inverter circuit for supplying the heating coil with a high-frequency current operates in response to an output signal from a detector which automatically detects the magnetic characteristics of the metallic material of the cooking vessel. As the high-frequency magnetic field is applied, a skin effect is produced within the metallic material of the vessel, so that the impedance for the magnetic field of the vessel is substantially fixed without regard to the wall thickness of the vessel.