Lithium–sulfur (Li-S) batteries are promising energy storage devices owing to their high energy density and the low cost of sulfur. However, they are still far from being applied commercially because of the detrimental capacity fade caused by the dissolution of lithium polysulfide (LPS) in liquid electrolyte. In this study, we introduced a new polymer binder having a redox-mediating function that assists in the reduction of soluble LPS to Li2S at the cathode to suppress the shuttle effect as well as enhance sulfur utilization. An amine group containing benzo(ghi)perylene imide (BPI) was synthesized and grafted onto poly(acrylic acid) to produce a redox-mediating polymer binder. An Li-S cell fabricated using the new redox-mediating polymer binder demonstrated a capacity decay retention of 0.036% per cycle up to 500 cycles at 0.5 C with a coulombic efficiency of 98%.