Lithium-sulfur batteries show great potential in the field of energy storage because of their high-energy density, but the shuttle effect of lithium polysulfide has seriously hindered their practical process. Quasi-solid-state electrolyte (QPE) is considered to be a promising alternative to traditional liquid electrolyte, which can improve the safety and cycling performance of lithium-sulfur batteries. Herein, a novel poly(vinyl carbonate-co-butyl acrylate) QPE with 3D crosslinked network (PEGDA-P(VCA-co-BA)) is designed to capture lithium polysulfide through a chemical adsorption of abundant ester groups. The PEGDA-P(VCA-co-BA) QPE exhibits high ionic conductivity of 2.9 mS cm−1. In order to synergize the beneficial effect of the PEGDA-P(VCA-co-BA) QPE, the nitrogen-doped carbon nanotube film-supported sulfur/Li cells are assembled with the QPE. As-assembled lithium-sulfur batteries show high initial capacity of 1080 mAh g−1 at 0.1 C, long cycle life (capacity retention of 715 mAh g−1 after 500 cycles) and superior rate performance.