The invention provides a dual-function catalyst and preparation thereof and application in a metal-air battery. The preparation method of the dual-function catalyst is characterized by comprising the steps that firstly, a manganese dioxide precursor is prepared; secondly, the manganese dioxide precursor, cobalt nitrate and carbon nano tubes with the mass ratio of 0.5-1:1:0.25-0.5 are weighed respectively and dissolved in 1-1.5 mol/L of ammonium hydroxide, ultrasonic dispersion is carried out for 0.5-1.5 hours, the mixture is then transferred into a high-pressure autoclave to be reacted for 3-6 hours at 140-160 DEG C and then is cooled to the room temperature, and the mixture is cleaned with deionized water for 3-5 times and then dried for 6-10 hours at 50-70 DEG C; after drying, roast is carried out in a muffle furnace at 350-450 DEG C for 0.5-1.5 hours, the mixture is ground into powder when the temperature is lowered to 60 DEG C, and the dual-function catalyst is obtained. The dual-function catalyst has both the efficient oxygen reduction performance and the efficient oxygen evolution performance in air.