Based on first principles density functional theory calculations we explore the energetics of the conversion of carbon mono and dioxide to methane over graphene oxide surfaces. Similar to therecently discovered hydration of various organic species over this catalyst, the transfer of hydrogenatoms from hydroxyl groups of graphene oxide provide a step by step transformation hydrogenationof carbon oxides. Estimated yields of modeled reactions at room temperature are about 0.01% for thecarbon mono and dioxide. For the modeling of graphene oxide/metal oxide composites, calculationsin the presence of MO₂(where M = V, Cr, Mn, Fe) have been performed. Results of these calculations demonstrate significant decreases of the energy costs and increases of reaction yields to 0.07%, which is comparable to the efficiency of these reactions over platinum and ruthenium-based photocatalysts. Increasing the temperature to the value 100°C should provide the total conversion of carbon mono and dioxides.