The design of highly efficient catalysts to enhance the kinetics of oxygen reduction (OER) and oxygen evolution (ORR) reactions is the key issue for the development of high-performance Zn-air battery. In this work, we report the design of Co-CoTe heterostructured fibers as the bifunctional oxygen catalyst for Zn-air battery. Firstly, the theoretical analysis was carried out on Co-CoTe heterostructure. The large work function difference is favorable to construct strong interfacial built-in electric field (BIEF), and the low energy barrier endows high catalytic activities. Moreover, the in-situ grown carbon shell was designed to build “core–shell” Co-CoTe/C unit to realize its high performance. They assemble the Co-CoTe@HFS fiber with good self-supporting and flexible features. Taken the advantages of the strong BIEF, the “core–shell” basic unit, and the freestanding substrate, the Co-CoTe@HFS fiber achieves the good electrocatalytic properties and high reliability. The full Zn-air battery (ZAB) with the Co/CoTe@HFS air cathode achieves the high peak power density and cycling stability over long-term cycling. Therefore, this work provides a clue to design bifunctional oxygen catalysts for high-performance ZABs.