Provided is a fuel cell including an anode electrode, a cathode electrode, and an electrolyte/ion exchange membrane between the anode electrode and the cathode electrode. The cathode electrode uses an iron redox couple as an oxidizer. The iron redox couple is regenerated by an oxidizing substance. The fuel cell does not need a noble metal catalyst, is thus economical in manufacturing costs, and has high power density, thereby improving energy conversion efficiency. Furthermore, the fuel cell is capable of decomposing an oxidizing substance, such as NOx, Cl2, Br2, or O3.