The invention discloses exposed high-index crystal face Co3O4 and a preparation method and application thereof. The preparation method comprises the following steps: adding an appropriate amount of glycerinum into a cobalt nitrate solution, and performing stirring for complete dissolution; adding a sodium carbonate solution for adjusting to be alkaline, and performing a reaction under the room temperature to obtain a precursor sediment; and performing suction filtration, washing, drying and roasting on the sediment to obtain selectively exposed (311) high-index crystal face Co3O4. By taking cobalt nitrate as a cobalt source, a small amount of glycerinum as a structure-directing agent, and sodium carbonate as a precipitator, a Co3O4 material with a selectively exposed high-index crystal face, a smaller grain size and a higher specific surface area is prepared by a simple chemical precipitation method. The Co3O4 material obtained by the method shows excellent activity in a catalytic combustion reaction of propane. The preparation method has the characteristics of easily accessible raw material, simple process, high catalyst activity and the like, and has a very good application prospect.