In this study, we synthesized a molybdenum complex, [MoO2(L)(H2O)] (1), utilizing a Schiff base ligand H2L (I), which was formed by reacting 3,5-di-tert-butyl-2-hydroxybenzaldehyde with the mono hydrazide of terephthalic ester in a methanolic solution. This complex was subsequently immobilized on a functionalized graphene oxide surface (APTES@GO), prepared using 3-aminopropyltriethoxysilane (APTES) and graphene oxide (GO), yielding the supported complex [MoO2(L)(H2O)]@APTES@GO (2). Both complexes were characterized through various analytical techniques, with single-crystal X-ray diffraction (SC-XRD) being specifically employed for complex 1. The catalytic activities of the homogeneous and heterogeneous complexes were assessed for their peroxidase-like and catechol oxidase-like functions, particularly in the oxidation of 3,3′-diaminobenzidine (DAB) and 3,5-di-tert-butylcatechol (3,5-DTBC) in the presence of hydrogen peroxide. Both complexes exhibited excellent catalytic efficiency (Kcat) and substrate binding affinity (KM), comparable to natural enzymes. Additionally, the supported complex demonstrated good reusability, maintaining its catalytic activity over five consecutive cycles.