An air filter mounting/demounting apparatus for a microwave oven having easy mounting and demounting of the air filter is provided. The apparatus includes a base plate having an inlet port through which air is admitted to serve as a hood, an air filter installed at a position corresponding to the inlet port and configured to filter foreign substances being admitted through the inlet port, an air filter bracket coupled to the base plate, an air filter holder at which the air filter is assembled coupled to the air filter bracket to enable a sliding movement along the guide rail, a latch unit configured to be coupled to the base plate to maintain and release engagement of the air filter holder aged, and a spring installed at an inside the latch unit to deliver an elastic force to the air filter holder.