The dissolution and shuttle of the intermediate lithium polysulfides are major issues which restrict practicality of lithium-sulfur batteries. Herein, self-supporting graphene/acid-treated multi-walled carbon nanotube organic foam-supported sulfur (oGCTF@S) composites are fabricated by solvothermal reaction followed by electrochemical deposition. The oGCTF@S composites can provide high electronic conductivity and much void space for accommodating volume change of sulfur and confine dissolution of the polysulfides by physical adsorption. In addition, a novel quasi-solid-state polymer electrolyte (QPE) of poly(butyl acrylate)/poly(ethylene glycol) diacrylate (P(BA-co-PEGDA))/LiTFSI-DOL/DME is prepared to further suppress the polysulfides shuttle through chemical adsorption with oxygen-containing functional groups. The lithium-sulfur battery assembled by oGCTF@S composites cathode and QPE shows a high initial discharge capacity of 1033 mAh g(-1), and the capacity can retain 834 mAh g(-1) after 200 cycles at 0.1 C, which is much more stable than that with the commercial separator and liquid electrolyte (LE).