Catalytic membrane reactors (CMRs) for water-gas shift (WGS) reaction can improve reaction efficiency by breaking the reaction equilibrium and have been recognized as a promising approach for simultaneous blue H2 production and CO2 capture. However, state-of-the-art WGS-CMRs are mainly based on H2-selective inorganic membranes (such as palladium and zeolites) that are expensive and difficult to produce on a large scale. On the other hand, carbon molecular sieve (CMS) membranes can be fabricated from polymeric precursors with excellent processability, and they can exhibit strong size-sieving ability and excellent thermal stability to achieve superior H2/CO2 separation in the CMRs. In this work, we first developed thin-film composite (TFC) membranes containing a CMS selective layer derived from acid-doped polybenzimidazole (PBI) using a facile and scalable approach. The TFC membranes exhibited stable H2/CO2 separation performance with H2 permeance of 30 GPU, H2/CO2 selectivity of 86, and H2/CO selectivity of 204 at 220 ℃ under WGS reaction conditions for 48 hours. Second, the membranes with an average effective area of 8 cm2 were assembled into the CMR containing a commercial WGS catalyst, and they were then evaluated for WGS reactions from 180 to 250 ℃. The CO conversion in the CMRs was thoroughly investigated as a function of steam-to-CO ratio, H2 content, temperature, pressure, and gas hourly space velocity (GHSV). The CMRs exhibited higher CO conversions than traditional packed bed reactors (PBR). For example, at a GHSV of 20,000 h-1 and 220 ℃, CO conversion in CMR is 71%, higher than that (60%) in PBR. More importantly, the continuous H2 production in the CMR was stable for up to 100 hours, demonstrating the great promise of highly H2-selective carbon membranes in WGS-CMRs.