The development of bifunctional oxygen electrocatalysts with high efficiency, high stability, and low cost is of great significance to the industrialization of rechargeable Zn–air batteries. A widely accepted view is that the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER) follow different catalytic mechanisms, and accordingly they need different active sites for catalysis. Transition metal elements have admirable electronic acceptance ability for coordinating with reactants, and this can weaken the bond energy between reactants, thus promoting the ORR or OER reactions. Herein, the ORR and OER activities of different transition metal supported nitrogen-doped carbon nanotubes were systematically studied and compared. The optimal catalyst for synchronous ORR and OER was obtained by pyrolyzing melamine, cobalt nitrate, and nickel nitrate on carbon nanotubes, called cobalt–nickel supported nitrogen-mixed carbon nanotubes (CoNi–NCNT), which were equipped with two types of high-performance active sites—the Co/Ni–N–C structure for the ORR and CoNi alloy particles for the OER—simultaneously. Remarkably, the optimized CoNi–NCNT exhibited a satisfactory bifunctional catalytic activity for both the ORR and OER. The value of the oxygen electrode activity parameter, ΔE, of CoNi–NCNT was 0.81 V, which surpasses that of catalysts Pt/C and Ir/C, and most of the non-precious metal-based bifunctional electrocatalysts reported in previous literatures. Furthermore, a specially assembled rechargeable Zn–air cell with CoNi–NCNT loaded carbon paper as an air cathode was used to evaluate the practicability. As a result, a superior specific capacity of 744.3 mAh/gZn, a peak power density of 88 mW/cm2, and an excellent rechargeable cycling stability were observed, and these endow the CoNi–NCNT with promising prospects for practical application.