Organosulfur polymers are a unique class of cathode materials for rechargeable lithium batteries. They are abundant, rich in structure, and easy for synthesis. Here, we report a new class of organosulfur polymers synthesized by condensation reactions between 1,3,5-benzenetrithiol (BTT) and elemental sulfur with three different molar ratios (i.e., 1:1.5, 1:3.0, and 1:4.5) in carbon disulfide solution without heating and additional catalyst. Removal of H₂S leads to the linkage of S-S bonds, forming hyperbranched polymers. When the BTT: sulfur molar ratio is 1:4.5, the polymer has a high theoretical specific capacity of 901.7 mAh g⁻¹. We have studied their structures and compositions through a series of material characterizations, and conducted an in-depth discussion on their electrochemical behavior in rechargeable lithium batteries. Excellent cycling performance of these materials shows great potential for practical application.