Solid-supported graphene is a typical configuration of electrochemical devices based on single-layer graphene. Therefore, it is necessary to understand the electrochemical features of such heterostructures. In this work, we theoretically investigated the effect of the metal type on the nonadiabatic electron transfer (ET) at the metal-supported graphene using DFT calculations. We considered five metals Au, Ag, Pt, Cu, and Al on which graphene is physically adsorbed. It is shown that all metals catalyze the ET. The electrocatalytic effect increases in the following series Al < Au ≲ Ag ≈ Cu < Pt. The enhanced ET in the presence of the metal substrate is explained by the hybridization of metal and graphene states, due to which the coupling between the reactant in an electrolyte and metal is increased. Metal-dependent electrocatalytic effect is explained both by different densities of states at the Fermi level of the systems and by differences in the behaviour of the tails of hybridized wave functions in the electrolyte region. The shift of the Fermi level with respect to the Dirac point in graphene when charging at the metal/graphene/electrolyte interface does not affect the kinetics due to the small contribution of graphene states to the electron transfer.