A novel configuration of two electrodes containing electrocatalysts for oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) pressed into a bifunctional air electrode is designed for rechargeable Zn–air batteries. MOC/25BC carbon paper (MOC consisting of α-MnO2 and XC-72 carbon black) and Fe0.1Ni0.9Co2O4/Ti mesh on this air electrode mainly serve as the cathode for the ORR and the anode for the OER, respectively. The morphology and physicochemical properties of Fe0.1Ni0.9Co2O4 are investigated through scanning electron microscopy, inductively coupled plasma-mass spectrometry, and X-ray diffraction. Electrochemical studies comprise linear sweep voltammetry, rotating ring-disk electrode voltammetry, and the full-cell charge–discharge–cycling test. The discharge peak power density of the Zn–air battery with the unique air electrode reaches 88.8 mW cm−2 at 133.6 mA cm−2 and 0.66 V in an alkaline electrolyte under an ambient atmosphere. After 100 charge–discharge cycles at 10 mA cm−2, an increase of 0.3 V between charge and discharge cell voltages is observed. The deep charge–discharge curve (10 h in each step) indicates that the cell voltages of discharge (1.3 V) and charge (1.97 V) remain constant throughout the process. The performance of the proposed rechargeable Zn–air battery is superior to that of most other similar batteries reported in recent studies.