Magnesium-ion batteries (MIBs) are promising candidate of energy storage due to the superiorities of no dendrite formation and low-cost. MXenes, new members in the 2D material family with excellent electrochemical and mechanical properties, are favorable electrode materials for MIBs. In this study, we evaluate the performance of functionalized MXenes (Ti(2)CO(2)and V2CO2)/graphene heterostructures with epoxy or hydroxyl groups as anode of MIBs using first-principles calculations. All functionalized MXene/graphene heterostructures exhibit great potentials for two-layer Mg intercalation with the interlayer expansions less than 10% and the open-circuit voltages always positive, compared with the pristine graphene heterostructures with >20% expansion and negative voltages, when intercalating the second layer Mg. Mg diffusion barriers (<0.3 eV) in functionalized MXene/graphene heterostructures are also significantly decreased than MXene/graphene (0.6-0.7 eV) due to the reduction of geometric constraint. The functionalized MXene/graphene heterostructures are expected to be promising anode materials for MIBs to enhance the specific capacity and charge/discharge rate.