Covalent organic frameworks (COFs) have shown promise as bifunctional catalysts to simultaneously mitigate shuttle effects and Li dendrite issues of lithium-sulfur (Li-S) batteries. However, the inherent low conductivity of the COFs has significantly limited their catalytic activity and stability. Herein, bifunctional catalytic activity and durability of the COF/MXene heterostructure are activated by tuning the surface curvatures of COFs interfaced with MXene. The increased curvature of COFs could induce enhanced electron delocalization and alter heterostructure geometry, which in turn strengthens lithium polysulfide adsorption, lowers energy barriers, and stabilizes catalytic sites to promote sulfur redox reactions. Concurrently, the hierarchical COF/MXene structure improves electrolyte penetration and wettability, facilitates rapid ion transport, and homogenizes the Li-ion flux distribution, thus achieving uniform lithium deposition. Consequently, the 1D-COF/MXene Li-S batteries demonstrate a high-rate capacity of 926 mA h g