Single-atom catalysts show good oxygen reduction reaction (ORR) performance in metal-air battery. However, the symmetric electron distribution results in discontented adsorption energy of ORR intermediates and a lower ORR activity. Herein, Fe-Co dual-atom catalyst with FeN3-CoN3 configuration was prepared by encapsulating nitrogen-rich ion (triethylenediamine cobalt complex, [Co(en)3]3+) in Fe based MOF cage to greatly enhance ORR performance. Due to the confinement effect of the MOF cage, the encapsulated [Co(en)3]3+ is closer to Fe of MOF, thus easily generating FeN3-CoN3 sites. The FeN3-CoN3 sites can break the symmetric electron distribution of single-atom sites, optimizing adsorption energy of oxygen intermediate. Thus, FeCo-NC exhibits extraordinary ORR activity with a high half-wave potential of 0.915 V and 0.789 V in alkaline and acidic electrolyte, respectively, while it was 0.874 V and 0.79 V for Pt/C. The liquid and solid Zn-air batteries with FeCo-NC as cathode show higher peak power density and specific capacity. DFT results indicate that FeN3-CoN3 site can reduce the reaction energy barrier of the rate-determining step resulting in an excellent ORR performance.