Here we reported a causal relationship between the molecular structure of binaphthol-based polyimide precursor and the pore-size distribution of the derived carbon membrane. The binaphthol-based polyamide acid is synthesized from 2,2′-diol-1,1′-binaphthyl-6,6′-diamine and 4,4′-(hexafluoroisopropylidene)diphthalic anhydride (6FDA). Then, an azeotropic imidiaztion method was used to synthesize the polyimide with naphthol groups (XS1). When the imidization is carried out by using acetic anhydride, the polyimide with acetyl groups (XS4) is achieved. The CMS membranes prepared by pyrolyzing XS1 and XS4 at 500, 550, and 600 ℃ are named using the temperature as the suffix, such as XS1-500. Their pore evolution has been investigated using TGA, FTIR, XRD, and Raman measurements. The trimodal pore-size distribution is in the carbon molecular sieve (CMS) membranes derived from XS4 and the CMS ones derived from XS1 exhibit a bimodal pore structure. Among them, XS4-500 exhibits the highest gas permeabilities of 3332 barrer for CO2, 773 barrer for O2, and 119 barrer for N2. XS1-500 only affords the CO2, O2, and N2 permeabilities of 1086, 230, and 30.2 barrer. The esterification of naphthol not just disturbs the hydrogen bonds between polyimide chains but also affects the pore generation of the derived CMS membranes. Our work provides an effective way to enhance the gas permeability of a CMS membrane derived from the binaphthol-based polyimide.