A lithium-sulfur battery which includes an electrolyte containing lithium-ions, an anode and a cathode containing sulfur. The lithium-sulfur battery also contains a surface layer which is arranged between the anode and the cathode. The lithium-sulfur battery further includes areas on the cathode side which contain polysulfides. The surface layer of the lithium-sulfur battery contains at least one graphene layer which is permeable to lithium ions and impermeable to polysulfides.