CO2 capture and separation from natural and fuel gas are important industrial issues that refer to the control of CO2 emissions and the purification of target gases. Here, a novel non-planar g-C12N8 monolayer that could be synthesized via the supramolecular self-assembly strategy was identified using DFT calculations. The cohesive energy, phonon spectrum, BOMD, and mechanical stability criteria confirm the stability of the g-C12N8 monolayer. Our DFT calculations and MD simulations designate the g-C12N8 monolayer to perform as a superior CO2 separation membrane from CH4 and C2H2 gas owing to the high CO2 permeability and selectivity. Specifically, the CO2 permeability ranges from 1.21 × 107 to 1.53 × 107 GPU, while the selectivity of CO2/CH4 and CO2/C2H2 is 3.03 × 103 and 3.10 × 102 at 300 K, respectively, much higher than the Robeson upper bound and most of the reported 2D membranes, and even at high temperatures, the g-C12N8 monolayer-based CO2 separation membranes could operate with high performance. Further, at room temperature, the permeated CO2 gas can adsorb on the g-C12N8 surface with moderate adsorption energy and high capacity. These results indicate that the g-C12N8 membrane exhibits high performance for controlling CO2 capture and separation, which inevitably injects a new alternative of novel 2D membranes for CO2 separation and capture from CH4 and C2H2 in light of further experimental and theoretical research.