The effect of a gold underlayer on the outer-sphere non-adiabatic electron transfer on a graphene surface is investigated theoretically using both periodic and cluster DFT calculations. We propose a model that describes the alignment of energy levels and charge redistribution at the metal/graphene/redox electrolyte interface. Model calculations were performed for the [Fe(CN)6]3-/4- and [Ru(NH3)6]3+/2+ redox couples. It is shown that the gold support increases the rate constant of electron transfer. Gold electronic states hybridize with graphene wave functions, which provides an effective overlap with reactant orbitals outside the graphene layer and favors an increasing reaction rate. Although the Fermi level shift relative to the Dirac point in graphene depends significantly on the redox couple, this weakly affects the electron transfer kinetics at the Au(111)/graphene/electrolyte interface due to a small contribution of graphene states to the rate constant as compared to gold ones.