Block copolymer membranes can be applied to precise size-based separation because of their highly ordered surface morphology and adjustable pore sizes. However, there is a lower limit of the scale of block copolymer self-assembly; this makes it a challenge to tailor the pore size down to below 10 nm. In this study, poly(styrene-b-4-vinyl pyridine) membranes were modified to quaternized selective layers with pores smaller than 10 nm and were supported by poly(vinylidene fluoride) hollow fibers as the substrate to provide a high mechanical strength. Two reactants, methyl iodide and 2-chloroacetamide, were used in the quaternization. With this one-step chemical modification, the molecular weight cutoff was reduced from 190 to 8 kDa, and the surface pore sizes were narrowed down from 20-30 to 3 nm; this bridged the gap of tailored pore sizes down to below 10 nm. Such membranes are promising candidates for low-molecular-weight separation with high resolution.