Pyrolyzing metal–organic frameworks (MOFs) typically yield composites consisting of metal/metal oxide nanoparticles finely dispersed on carbon matrices. The blend of pseudocapacitive metal oxides and conductive metals, as well as highly porous carbon networks, offer unique opportunities to obtain supercapacitor electrodes with mutually high capacitances and excellent rate capabilities. Herein, we demonstrate nitrogen-doped carbon nanocuboid arrays grown on carbon fibers and incorporating cobalt metal and cobalt metal oxides. This composite was synthesized via pyrolysis of a chemical bath deposited MOF, cobalt-containing zeolite imidazole framework (Co–ZIF). The active materials for charge storage are the cobalt oxide and nitrogen-doped carbon. Additionally, the Co metal and the nanoporous carbon network facilitated electron transport and the rich nanopores in each nanocuboid shortened ion diffusion distance. Benefited from these merits, our Co–ZIF-derived electrode delivered an areal capacitance of 1177 mF cm−2 and excellent cycling stability of ~94% capacitance retained after 20,000 continuous charge–discharge cycles. An asymmetric supercapacitor prototype having the Co–ZIF-derived hybrid material (positive electrode) and activated carbon (negative electrode) achieved a maximal volumetric energy density of 1.32 mWh cm−3 and the highest volumetric power density of 376 mW cm−3. This work highlights the promise of metal–metal oxide–carbon nanostructured composites as electrodes in electrochemical energy storage devices.