In spite of the recent advancements, rational design and synthesis of non-precious metal oxygen redox catalysts for oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) in both alkaline and acidic media is still a crucial challenge for the development of rechargeable metal-air batteries and regenerative fuel cells. Heteroatom doped carbon-based materials exhibit a promising strategy to achieve the bifunctionality within one catalyst. Herein, we report a highly efficient Fe-N-C oxygen redox catalyst derived from a new class of Fe coordinated bis(imino)-pyridine ligand based polymer synthesized via Schiff base condensation between 2,6-diacetylpyridine and 1,8-diaminonaphthalene. The Fe-N-C catalyst prepared by this precursor without templates or supports is characterized by spherical structure, ultrahigh specific surface area up to 1796.0 m2/g, a high degree of graphitization and atomically dispersed five-coordinated Fe-N5 sites. These unique features endow the catalyst with outperforming performance for ORR and OER in terms of remarkable activity and stability in both alkaline and acidic media. The overall oxygen redox activity (ΔE = Ej=10 − E1/2) (0.70 V in alkaline media and 0.86 V in acidic media) of the catalyst for both ORR and OER is much higher than those of none precious metal catalysts previously reported. These outstanding features remark the great possibility of the introduced catalyst for the practical application.