The present invention relates to a composite cooker having a plurality of heat sources. The cooker, according to one embodiment of the present disclosure, may comprise: a housing having a cavity formed therein; door connected to the housing so as to open/close the cavity; a MW heating module for radiating microwaves to the cavity; an IH heating module for radiating a magnetic field toward the cavity; and a shielding member for enabling the magnetic field generated by the TH heating module to pass through, while blocking the microwaves radiated from the MW heating module. The shielding member may comprise carbon fiber.