Zeolitic imidazolate frameworks have stimulated great attention due to their potential applications in energy storage, catalysis, gas sensing, drug delivery etc. In this paper, the three-dimensional porous nanomaterial Co3O4/ZnCo2O4/CuO with hollow polyhedral nanocage structures and highly enhanced electrochemical performances was synthesized successfully by a zeolitic imidazolate framework-67 route. The composites hold the shape of the ZIF-67 templates well and the shell has multiple compositions. In the process, we first synthesized the nanostructure hydroxide precursors and then transformed them into the corresponding metal oxide composites by thermal annealing in air. In addition, the mass ratio of Zn to Cu in this material is discussed and optimized. We found that when the mass ratio is 3, the composite material has better electrochemical properties. When applied as an electrode material, Co3O4/ZnCo2O4/CuO-1 shows enhanced pseudocapacitive properties and good cycling stability compared with Co3O4/ZnCo2O4, Co3O4/CuO and Co3O4/ZnCo2O4/CuO-2, and Co3O4/ZnCo2O4/CuO-3. The assembled Co3O4/ZnCo2O4/CuO-1//AC hybrid device can be reversibly cycled in a large potential range of 0-1.6 V and can deliver a high energy density of 35.82 W h kg-1 as well as the maximum power density of 4799.25 W kg-1.