Copper catalysts have been extensively studied for CO oxidation at low temperatures. Previous findings on the stability of such catalysts, on the other hand, revealed that they deactivated badly under extreme circumstances. Therefore, in this work, a series of KCC−1-supported copper oxide catalysts were successfully prepared by impregnation method, of which 5% CuO/KCC−1 exhibited the best activity: CO could be completely converted at 120 °C. The 5% CuO/KCC−1 catalyst exhibited better thermal stability, which is mainly attributed to the large specific surface area of KCC−1 that facilitates the high dispersion of CuO species, and because the dendritic layered walls can lengthen the movement distances from particle-to-particle, thus helping to slow down the tendency of active components to sinter. In addition, the 5% CuO/KCC−1 has abundant mesoporous and surface active oxygen species, which are beneficial to the mass transfer and promote the adsorption of CO and the decomposition of Cu+–CO species, thus improving the CO oxidation performance of the catalyst.