Rational design and exploration of robust and low‐cost bifunctional oxygen reduction/evolution electrocatalysts are greatly desired for metal–air batteries. Herein, a novel high‐performance oxygen electrode catalyst is developed based on bimetal FeCo nanoparticles encapsulated in in situ grown nitrogen‐doped graphitic carbon nanotubes with bamboo‐like structure. The obtained catalyst exhibits a positive half‐wave potential of 0.92 V (vs the reversible hydrogen electrode, RHE) for oxygen reduction reaction, and a low operating potential of 1.73 V to achieve a 10 mA cm−2 current density for oxygen evolution reaction. The reversible oxygen electrode index is 0.81 V, surpassing that of most highly active bifunctional catalysts reported to date. By combining experimental and simulation studies, a strong synergetic coupling between FeCo alloy and N‐doped carbon nanotubes is proposed in producing a favorable local coordination environment and electronic structure, which affords the pyridinic N‐rich catalyst surface promoting the reversible oxygen reactions. Impressively, the assembled zinc–air batteries using liquid electrolytes and the all‐solid‐state batteries with the synthesized bifunctional catalyst as the air electrode demonstrate superior charging–discharging performance, long lifetime, and high flexibility, holding great potential in practical implementation of new‐generation powerful rechargeable batteries with portable or even wearable characteristic. Bamboo‐like FeCo alloy encapsulated in nitrogen‐doped carbon nanotubes exhibits superior catalytic oxygen reduction and oxygen evolution performance than that of noble metal benchmarks, which benefits from the nitrogen‐rich and defect‐rich catalyst surface. The all‐solid‐state zinc–air batteries equipped by the synthesized materials show low charging/discharging overpotentials, long lifetime, and high flexibility, suitable for practical application.