Developing the catalysts that can efficiently degrade brominated volatile organic compounds (Br-VOCs) is a priority due to the low activity, the low product selectivity, and the low resistance to Br-poisoning. In this work, Co3O4/CeO2-Co3O4 hierarchical binary oxides were designed as a high-performance catalyst for the catalytic oxidation of dibromomethane (CH2Br2) as a model pollutant for Br-VOCs. The surface of carbon spheres was coated with a layer of CeO2 nanoparticles, and core-shell CSs@CeO2 were the precursors of Co3O4/CeO2?Co3O4 hierarchical binary oxides. Co3O4/CeO2-Co3O4(HS) had a hierarchical porous structure, there was a strong interaction between Co3O4 and CeO2·Co3O4/CeO2-Co3O4(HS) showed an excellent catalytic activity, and its T90 value was only 321 °C. Meanwhile, Co3O4/CeO2-Co3O4(HS) showed good stability for at least 30 h. Co3O4 provided the active sites for CH2Br2 oxidation, and the hierarchical porous structure and high specific surface area were conducive to the adsorption of CH2Br2 molecules. Meanwhile, CeO2 promoted the oxygen mobility of the composite and the oxidation performance of Co3O4- CH2Br2 molecular firstly adsorbed on Co3O4/CeO2-Co3O4(HS) surface, and dissociated to form the intermediates (i.e., formate species, and methoxy species), which were finally oxidized to CO and CO2, and Br species were removed in the form of HBr and Br2.