The measured reversible capacity of the single layer graphene electrode (SLG/Cu) in sodium-ion batteries is mostly due to the electrochemical response of the copper substrate. Display omitted •Single layer graphene (SLG) grown on copper foil is investigated as anode for sodium-ion batteries.•The amount of Na+ ions adsorbed/desorbed reversibly per surface area is very modest (<20μAhcm−2).•The reversible capacity of SLG is mostly due to the electrochemical response of copper substrate.•The results agree with calculations showing that Na+ ions adsorption on SLG is energetically unfavourable. In an attempt to find an adequate carbon material to achieve a successful reversible adsorption of Na+ ions, single layer graphene, is experimentally investigated in this work, for the first time, as anode for sodium-ion batteries. To this end, single layer graphene that was grown on copper foil by chemical vapor deposition was subjected to extended galvanostatic cycling and to cyclic voltammetry in the potential range of 0-2.8V versus Na/Na+. Regardless of the current density and electrolyte formulation used, the amount of Na+ ions adsorbed/desorbed reversibly per surface area (specific reversible cell capacity) was very modest and comparable to that obtained with bare copper electrodes of reference, thus suggesting that the reversible capacity of the single layer graphene electrode is mostly due to the electrochemical response of the copper substrate. These experimental results clearly agree with recent theoretical calculations showing that the adsorption of Na+ ions on the surface of single layer graphene is energetically unfavourable unless that surface includes significant defects density.