The one-step highly selective oxidation of cyclohexane into cyclohexanone and cyclohexanol as the essential intermediates of nylon-6 and nylon-66 is considerably challenging. Therefore, an efficient and low-cost catalyst must be urgently developed to improve the efficiency of this process. In this study, a Co3O4–CeO2 composite oxide catalyst was successfully prepared through ultrasound-assisted co-precipitation. This catalyst exhibited a higher selectivity to KA-oil, which was benefited from the synergistic effects between Co3+/Co2+ and Ce4+/Ce3+ redox pairs, than bulk CeO2 and/or Co3O4. Under the optimum reaction conditions, 89.6% selectivity to KA-oil with a cyclohexane conversion of 5.8% was achieved over Co3O4–CeO2. Its catalytic performance remained unchanged after five runs. Using the synergistic effects between the redox pairs of different transition metals, this study provides a feasible strategy to design high-performance catalysts for the selective oxidation of alkanes.