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Inspired by the advantages of bi-atom catalysts and recent exciting progresses of nanozymes, by means of density functional theory (DFT) computations, we explored the potential of metal dimers embedded in phthalocyanine monolayers (M2-Pc), which mimics the binuclear centers of methane monooxygenase, as catalysts for methane conversion using H2O2 as an oxidant. In total, 26 transition metal (from group IB to VIIIB) and four main group metal (M = Al, Ga, Sn and Bi) dimers were considered, and two methane conversion routes, namely *O-assisted and *OH-assisted mechanisms were systematically studied. The results show that methane conversion proceeds via an *OH-assisted mechanism on the Ti2-Pc, Zr2-Pc and Ta2-Pc, a combination of *O- and *OH-assisted mechanism on the surface of Sc2-Pc, respectively. Our theoretical work may provide impetus to developing new catalysts for methane conversion and help stimulate further studies on metal dimer catalysts for other catalytic reactions.