Mesoporous MnCo2O4 with hierarchical structures were synthesized from a dual-metal zeolitic-imidazolate framework (ZIF) as precursor. The corresponding heterometallic ZIF was synthesized by mixing manganese(II) and cobalt(II) ions in the presence of 2-methylimidazole as linker. Calcination of the intermediate ZIF in air affords the nanosized mesoporous manganese cobaltite with spinel crystal structure. The obtained nanomaterials were characterized by a combination of physico-chemical and spectroscopic techniques. The mesoporous spinel MnCo2O4 nanomaterials show the peroxidase-like activity in oxidation of o-phenylenediamine (OPD) at room temperature. Based on the efficient peroxidase-like activity, the mesoporous MnCo2O4 nanocatalyst/ODP substrate system was used for the determination of H2O2 concentration in aqueous solution. This report also includes the result of detailed kinetic study of the catalytic oxidation reaction. The mesoporous MnCo2O4 with large surface area showed higher catalytic activity in oxidation of OPD compared to that of natural peroxidase as well as the individual components Co3O4 and MnO2 nanoparticles. The constructed colorimetric H2O2 sensor based on the mesoporous MnCo2O4/OPD system has a wide linear range of 0.5-120 mM and a low detection limit of 0.2 mM.