Sulfur cathodes in lithium-sulfur (Li-S) batteries still suffer from their low electronic conductivity, undesired dissolution of lithium polysulfide (Li2S n , 3 ≤ n ≤ 8) species into the electrolyte, and large degree volume change during the cycle. To overcome these problems, an effective encapsulation for the sulfur cathode is necessary. By means of particle swarm optimization (PSO) and density functional theory (DFT), we have predicted a stable metallic two-dimensional sp 2-hybridized carbon allotrope (DHP-graphene). This carbon sheet can prevent S atoms from cathode entering electrolyte. However, Li-ions can shuttle freely due to the increasing difference in Li-ions concentration between electrolyte and cathode along with the potential difference between cathode and anode during charge-discharge cycles. In addition, versatile electronic band structures and linear dispersion are found in DHP-graphene nanoribbons but only metallic band structure occurs for DHP-graphene nanotubes.