A method of preparing a graphene-sulfur nanocomposite for a cathode in a rechargeable lithium-sulfur battery comprising thermally expanding graphite oxide to yield graphene layers, mixing the graphene layers with a first solution comprising sulfur and carbon disulfide, evaporating the carbon disulfide to yield a solid nanocomposite, and grinding the solid nanocomposite to yield the graphene-sulfur nanocomposite. Rechargeable-lithium-sulfur batteries having a cathode that includes a graphene-sulfur nanocomposite can exhibit improved characteristics. The graphene-sulfur nanocomposite can be characterized by graphene sheets with particles of sulfur adsorbed to the graphene sheets. The sulfur particles have an average diameter of less than 50 nm.