The development of non-noble metal carbon electrocatalysts is of great significance to the development of fuel cell, metal–air battery and water-splitting technology. In this work, a highly active Co–N-doped graphene bifunctional electrocatalyst (Co–N–C/rGO) was prepared by a very mild and simple method. With graphene oxide as the substrate, gluconic acid acts as a dispersion of cobalt and an additional carbon source, while urea acts as a nitrogen source and anchoring cobalt. Co–N–C/rGO showed excellent catalytic performance for the ORR, which even exceeded that of commercial Pt/C. In 0.1 M KOH, the onset potential and half-wave potential of Co–N–C/rGO are 1.04 V and 864 mV, respectively, which are higher than those of most of the similar carbon materials reported. Compared with Pt/C, the half wave potential loss is reduced by 35 mV, and it still shows obvious four-electron transfer characteristics and higher Tafel slope performance. Co–N–C/rGO-based primary liquid ZABs display a higher galvanostatic discharge capacity as well as higher power density. Moreover, we improved the traditional PVA electrolyte, and designed and prepared a PVA + PEO + GO electrolyte with better performance. The flexible ZABs fabricated using air electrodes containing Co–N–C/rGO and this solid electrolyte demonstrate good performance, with a high open circuit potential (1.49 V) and large peak power density (57 mW cm⁻²). In addition, the good HER catalytic performance of Co–N–C/rGO is characterized by a low Tafel slope of 42 mV dec⁻¹ and an overpotential of 220 mV at a current density of 10 mA cm⁻².