The hybrid metal-organic frameworks (MOFs) with different Zn2+/Co2+ ratios are synthesized at room temperature with deionized water as the solvent. This use of deionized water can increase the yield of hybrid MOFs (up to 65–70%). After the pyrolysis, the obtained nanoporous carbons (NPCs) show a decrease in the surface area, in which the highest surface area is 655 m2 g−1. The as-prepared NPCs are subjected to activation with KOH in order to increase their surface area and convert cobalt nanoparticles (Co NPs) to Co oxides. These activated carbons are applied to electrical double-layer capacitors (EDLCs) and pseudocapacitors due to the presence of CoO and Co3O4 nanoparticles in the carbon framework, leading to significantly enhanced specific capacitance as compared to that of pristine NPCs. This synthetic method can be utilized in future research to enhance pseudocapacitance further while maintaining the maximum surface area of the carbon materials.