The invention discloses a preparation method of a zinc-air battery catalyst. The preparation method comprises the following steps of: S1, adding 2, 5-dihydroxyterephthalic acid and polyacrylonitrile into N, N-dimethylformamide, carrying out ultrasonic dissolution, and then transferring a solution into an injection pump, and performing electrostatic spinning on an electrostatic spinning receiving roller so as to obtain a layer of fiber membrane I; S2, adding cobalt nitrate hexahydrate and polyacrylonitrile into N, N-dimethylformamide, performing ultrasonic dissolution, then transferring a solution into an injection pump, and performing electrostatic spinning on the fiber membrane I to obtain a layer of fiber membrane II; S3, taking down the fiber membrane II from the receiving roller, cutting the fiber membrane II into 2cm*2cm membranes, stacking the fiber membranes, placing the stacked fiber membranes in a 25mL high-pressure reaction kettle, adding a mixed solvent of which the liquid surface is higher than the height of the fiber membranes, pressing a metal block on the stacked fiber membranes to prevent the fiber membranes from floating, carrying out ultrasonic treatment, performing a reaction at 120-135 DEG C for 24-30 hours, performing cooling, filtering and drying to obtain a precursor; and S4, uniformly mixing the precursor obtained in the step S3 with calcium salt, then putting the mixture into a tubular furnace, and calcining the mixture in a mixed gas atmosphere to obtain the catalyst Co-MOF-74 (at) C/Ca.