Partial oxidation of methane (CH4) to methanol (CH3OH) remains a great challenge in the field of catalysis due to its low selectivity and productivity. Herein, Ag-O-Ag/graphene and Cu-O-Ag/graphene composite catalysts are proposed to oxidize methane (CH4) to methanol (CH3OH) by using the first-principles calculations. It is shown that reactive oxygen species (μ-O) on both catalysts can activate the C-H bond of CH4, and in addition to CH4 activation, the catalytic activity follows the order of Ag-O-Ag/graphene (singlet) > Ag-O-Ag/graphene (triplet) ≈ Cu-O-Ag/graphene (triplet) > Cu-O-Ag/graphene (singlet). For CH3OH* formation, the catalytic activity follows the order of Cu-O-Ag/graphene (triplet) > Ag-O-Ag/graphene (triplet) > Ag-O-Ag/graphene (singlet) > Cu-O-Ag/graphene (singlet). It can be inferred that the introduction of Cu not only reduces the use of noble metal Ag but also exhibits a catalytic effect comparable to that of the Ag-O-Ag/graphene catalyst. Our findings will provide a new avenue for understanding and designing highly effective catalysts for the direct conversion of CH4 to CH3OH.