The invention relates to a nickel manganese/carbon nanotube composite catalyst and preparation and application thereof. The bifunctional catalyst comprises a carbon nanotube and nickel manganese (NiMnO4) spinel. A manganese dioxide precursor, nickelous acetate and the carbon nanotube are dissolved in ammonia water and undergo ultrasonic dispersion, undergo a hydrothermal reaction for 3-6 h at 130-150 DEG C, are cooled to room temperature, cleaned, dried and calcinated, and the nickel manganese/carbon nanotube composite catalyst is obtained. The nickel manganese/carbon nanotube composite catalyst is applied to an air electrode of a metal-air battery. The nickel manganese/carbon nanotube composite catalyst has efficient oxygen reduction performance and efficient oxygen evolution performance and can be applied to metal-air batteries.