Recently, the development of high-performance bifunctional oxygen catalysts integrated with flexible conductive scaffolds for rechargeable metal-air batteries has attracted considerable interest, driving by fast-growing wearable electronics. Herein, we report a flexible bifunctional oxygen catalyst thin film consisting of Co–N–C bifunctional catalysts embedding in carbon nanotube (CNT) networks. The catalyst is readily prepared by pyrolysis of cobalt-based zeolitic imidazolate frameworks (ZIF-67) that are in-situ synthesized in CNT networks. Such catalyst film demonstrates very high catalytic activities for oxygen reduction (onset potential: 0.91 V, and half-wave potential: 0.87 V vs. RHE) and oxygen evolution (10 mA cm−2 at 1.58 V) reactions, high methanol tolerance property, and long-term stability (97% current retention). Moreover, our integrated catalyst film shows very good structure flexibility and robustness. Based on the obtained film air electrodes, flexible Zn–air batteries demonstrate low charging and discharging overpotentials (0.82 V at 1 mA cm−1) and excellent structure stability in the bending tests. These results indicate that presently reported catalyst films are potential air electrodes for flexible metal–air batteries.