(57) An improved grill/convection microwave oven and a convection cooking method thereof which are capable of simultaneously operating a convection heater and a grill heater in the convection cooking mode without using a damper system, for thus reducing the number of parts of the system, whereby it is possible to reduce the fabrication cost, which includes a grill heater and convection heater for a cooking operation, a magnetron for a microwave cooking, a cooking compartment for cooking food therein, a circulation motor for circulating heat generated by the convection heater, an oven lamp, a turntable motor, and a fan motor connected parallel with the circulation motor and controlled by one relay, and an air duct communicating with a cooking compartment air inlet, so that an air is introduced by the fan motor, and cools the magnetron, and then the thusly cooled air is introduced into the cooking compartment.