Five Cu-Mn complex-oxide catalysts supported on cordierite (COR) monolithic, Cu-Mn-O/Al2O3/COR, Cu-Mn-Ce-O/Al2O3/COR, Cu-Mn-Zr-O/Al2O3/COR, Cu-Mn-La-O/Al2O3/COR, and Cu-Mn-Ce-Zr-O/Al2O3/COR, for the catalytic combustion of lean methane were prepared by wetness impregnation using cordierite as the support. The effect of promoters such as CeO2, ZrO2, La2O3, and CeO2-ZrO2, on the structure and properties of Cu-Mn-O/Al2O3 was characterized by X-ray photoelectron spectroscopy, H-2 temperature-programmed reduction, and N-2 adsorption-desorption. The catalytic performance of lean methane catalytic combustion over these catalysts was evaluated in a fixed-bed reactor. The results showed that with the introduction of CeO2, ZrO2, La2O3, and CeO2-ZrO2 as the promoter to Cu-Mn-O/Al2O3/COR, the specific surface area of the catalysts increases obviously, resulting in an enhancement of active component dispersion and oxygen species concentration on the catalyst surface. Therefore, the surface oxidation reactivity of the catalysts is improved. Besides, the pore structure of the catalysts is also adjusted well, which is beneficial for matching the diffusion-reaction coupling behavior on the catalyst. The activity of Cu-Mn-O/Al2O3/COR, especially the low-temperature activity remarkably increases with the promoter addition. Among the tested promoters, ZrO2 shows the best promoting effect. The methane conversion over Cu-Mn-Zr-O/Al2O3/COR monolithic catalyst is up to 90% under the conditions of 570 degrees C and GHSV = 20000 h(-1).