Hierarchical porous multi-phase Ni–Zn–Co oxide/hydroxide is synthesized by using metal-organic framework-5 (MOF-5) as the template. Hierarchical porous carbon is obtained by the facile direct decomposition of the MOF-5 framework with phenolic resin. The structures and textures are characterized by X-ray diffraction, high-resolution transmission electron microscopy, scanning electron microscopy, and nitrogen sorption at 77K. An asymmetric capacitor incorporating the Ni–Zn–Co oxide/hydroxide as the positive electrode and the porous carbon as the negative electrode is fabricated. A maximum energy density of 41.65Whkg−1 is obtained, which outperforms many other available asymmetric capacitors. The asymmetric capacitor also shows a good high-rate performance, possessing an energy density of 16.62Whkg−1 at the power density of about 2900Wkg−1.