Disclosed is a method for preparing a platinum-manganese dioxide/carbon complex for a positive-electrode material of a lithium-air battery. More specifically, a manganese dioxide/carbon complex is prepared by dispersing carbon in a manganese dioxide precursor solution and applying microwaves, filtering and drying to the resulting solution. Next a platinum-manganese dioxide/carbon complex is prepared by dispersing the manganese dioxide/carbon complex in ethylene glycol, adding a platinum precursor and applying microwaves to the resulting solution. The platinum-manganese dioxide/carbon complex synthesized according to the present invention exhibits lower overvoltage and higher current density in oxygen reduction and oxidation reactions as compared to either a manganese dioxide/carbon complex or a platinum/carbon complex.