Catalysts with embedded and functionalized elements used for the effective control of oxygen-reduction (ORRs) and oxygen-evolution reactions (OERs) are the key to developing high-performance rechargeable Zn–air batteries (ZABs). Here, carbon nanotube-grafted, Co–Fe embedded, nitrogen-doped porous carbon nano-frameworks (CNT–Co–Fe/NC) were synthesized through the carbonization of Fe-doped zeolitic imidazolate frameworks and vulcanization of the CNT–Co–Fe/NC to form CNT–CoS2–Fe/NC. The CNT–CoS2–Fe/NC exhibited a superior OER performance with an overpotential of only 1.637 mV at a current density of 10 mA/cm2 and a Tafel slope of 197 mV/dec (which, for RuO2, is 112 mV/dec), whereas the CNT–Co–Fe/NC showed an excellent ORR performance with a Tafel slope of 71 mV/dec (which, for 20 wt% Pt/C, is 91 mV/dec). A ZAB was developed with a hybrid catalyst of 50 wt% CNT–Co–Fe/NC and 50 wt% CNT–CoS2–Fe/NC in the cathode, and it achieved an excellent specific discharge capacity of 814 mAh/g at 50 mA/cm2, high power density of 245 mW/cm2, and outstanding cycle stability of over 1800 cycles (300 h) at 10 mA/cm2 with a very high retention of 95% and small potential gap of 0.68 V, compared to the corresponding values of 803.7 mAh/g, 215.3 mW/cm2, 900 cycles: retention 92%, and potential gap 0.837 V for 150 h for the ZAB with a hybrid catalyst of Pt/C + RuO2. It is hypothesized that the ZAB with the novel hybrid catalyst exhibits its excellent catalytic activity and durability as a result of the synergistic effect of the catalyst’s embedded heteroatoms and nitrogen–metal/carbon framework that enhances the ORR/OER performance, porous carbon nano-framework that enables rapid diffusion and electrical conduction, and carbon nanotubes that complete the external electrical connection between the catalysts.