The exploration of highly-efficient, low-cost bifunctional oxygen electrocatalysts for both oxygen reduction reaction (ORR) and oxygen evolution reactions (OER) is critical for renewable energy storage and conversion technologies (e.g., fuel cells and metal–air batteries). Here we report the design and fabrication of free-standing nitrogen-doped carbon nanotube (NCNT) arrays via a directed growth approach as a high-performance bifunctional oxygen electrocatalyst. By virtue of the unique hierarchical nanoarray structure, uniform N-doping and decreased charge-transfer resistance, the as-prepared NCNT array exhibits rather high activity and stability in both ORR and OER, even superior to the mono-functional commercial Pt/C (for ORR) and IrO2 (for OER). A flexible, rechargeable all-solid-state zinc–air battery is successfully fabricated by using this self-supporting NCNT electrode as air-cathode, which gives excellent discharge-charge performance and mechanical stability.