The invention discloses a catalyst for decomposing nitrous oxide and a preparation method of the catalyst. The catalyst is prepared by the deposition precipitation method. The method comprises the processes of preparing a deposit, washing, forming a deposit, activating through the catalyst, etc.; the catalyst comprises active ingredients, a carrier which is zirconium oxide, and additives, wherein the active ingredients include one or more than two of Co, Ni, Fe and Mn; the additives include one or more of cerium oxide, lanthanum oxide and barium oxide. A catalyst activity experiment shows that nitrous oxide can be completely catalytically decomposed into nitrogen and oxygen at the temperature ranging from 450 to 700 DEG C; therefore, the activation temperature is low, and the T50 (reaction temperature under conversion rate of 50%) is about 350 DEG C. The catalyst is high in activity and outstanding in heat resistance, has a wide operation window, and enables the concentration of nitrous oxide in industrial waste gas to be greatly reduced, and therefore, the environmental pollution is decreased; the catalyst is particularly suitable for N2O removal of a nitric plant and an adipic acid plant.