A compound heating apparatus includes a microwave generating unit and an infrared radiation generator disposed in a casing outwardly of a heating chamber of the casing. A light shield is disposed around the infrared radiation generator, and has a shield opening facing toward the heating chamber. A microwave blocker plate covers the shield opening. An air supply module is connected to the light shield to blow air to the light shield for causing heat radiant energy generated from the infrared radiation generator to pass acceleratedly by forced heat convection through microwave blocking holes of the microwave block plate to the heating chamber.