High-performance membranes have emerged as an energy-efficient alternative to absorption-based postcombustion carbon capture. So far, the techno-economic analyses have been centered around the polymeric membranes. Recently, nanoporous single-layer graphene (NSLG) membranes have yielded large CO2 permeance, making them attractive for capture. Herein, we assess the techno-economic feasibility of NSLG-based capture using an optimized process. The most suitable system to achieve recovery and purity of 90% comprises a double-stage process with (i) recycle of 2nd stage retentate, and (ii) multi-staged vacuum pumps for the permeate, including roots pumps in series with liquid-ring pumps and intermittent condensers for water vapor. The high CO2 permeance of NSLG makes the vacuum process without feed compression more economically competitive, even if the area required is higher. Attractive capture penalties are estimated despite a conservative membrane cost (500 $/m2): 41.2 and 31.8 $/tonCO2 from wet feeds with CO2 concentration of 10% and 13.5%, respectively, corresponding to energy penalty of 1.53 and 1.24 MJ/kgCO2. For steel and cement industries where CO2 concentration is favorably high (25%) but electricity cost is also higher (0.10–0.20 $/kWh), the capture penalty ranges from 28.0 to 46.0 $/tonCO2. Overall, the analysis shows that NSLG membranes are competitive with state-of-the-art processes for postcombustion capture.