Covalent organic frameworks (COFs) exhibit considerable potential in gas separations owing to their remarkable stability and tunable pore structures. Nevertheless, their application as gas separation membranes is hindered by limited size-sieving capabilities and poor processability. In this study, we propose a novel molecular weaving strategy that combines hydroxyl polymers and 2D TpPa-SO3H COF nanosheets, achieving high gas separation efficiency. Driven by the strong electrostatic interactions, the hydroxyl chains thread through the COF pores, effectively weaving and assembling the composites to achieve exceptional flexibility and high mechanical strength. The penetrated chains also reduce the effective pore size of COFs, and combined with the "secondary confinement effect" stemming from abundant CO2 sorption sites in the channels, the PVA@TpPa-SO3H membrane demonstrates a remarkable H2 permeance of 1267.3 GPU and an H2/CO2 selectivity of 43, surpassing the 2008 Robson upper bound limit. This facile strategy holds promise for the manufacture of large-area COF-based membranes for small-sized gas separations.