Nanomaterials with enzyme-like characteristics (nanozymes) have emerged as potential replacements for natural enzymes due to their potential to overcome several critical limitations of natural enzymes, including low stability as well as high costs in preparation and purification. Herein, we have developed hybrid nanostructures that incorporate cobalt oxide nanoparticles (Co₃O₄ NPs) and gold nanoclusters (AuNCs) through electrostatic attraction induced by simple incubation in an aqueous buffer for 2 hours. Owing to the synergistic effect of Co₃O₄ NPs and AuNCs, the constructed Co₃O₄/Au hybrid nanostructures yielded highly enhanced peroxidase-like activity and enabled rapid catalytic oxidation of a chromogenic substrate, 3,3',5,5'-tetramethylbenzidine (TMB), producing a blue colored solution depending on the amount of H₂O₂. Moreover, we observed catalytic activity of the Co₃O₄/Au hybrid over a broad pH range, especially at physiologically relevant pH in the range of 5.0-7.4, which is advantageous for applications in biological systems. Using the hybrid as peroxidase mimic, we successfully determined the level of target H₂O₂ or glucose by coupling with glucose oxidase with excellent specificity and sensitivity. Based on this study, we expect that Co₃O₄/Au hybrid nanostructures can serve as potent peroxidase mimics for the detection of clinically important target molecules.