A tray driving apparatus for a microwave oven and a microwave oven having the same including a speed changing unit for enhancing the cooking quality by periodically changing the rotational speed of the tray to more evenly radiate a microwave to food. The speed changing means includes a driving gear unit having a plurality of driving gears and mounted to the driving shaft; and a driven gear unit having a plurality of driven gears corresponding to respective driving gears of the driving gear unit, and mounted to the driven shaft. The gears of any one of the driving gear unit and the driven gear unit are portion gears which are gears having gear teeth on respective portions of outer peripheries thereof, the gear teeth of the portion gears are alternately disposed to each other one on another. Accordingly, upon a rotation of the driving shaft, each portion gear of any one of the driving gear unit and the driven gear unit are alternately meshed with a corresponding gear of the other one of the driving gear unit and the driven gear unit, to thereby change the rotational speed of the tray.