Three graphdiyne-like monolayers were designed by substituting one-third diacetylenic linkages with heteroatoms hydrogen, fluorine, and oxygen (GDY_X(, X= H, F, and O), respectively. The CO2/N-2/CH4 separation performance of the designed graphdiyne-like monolayers was investigated by using both first-principle density functional theory (DFT) and molecular dynamic (MD) simulations. The stabilities of GDY_X monolayers were confirmed by the calculated cohesive energies and phonon dispersion spectra. Both the DFT and MD calculations demonstrated that although the GDY_H membrane has poor selectivity for CO2/N-2/CH4 gases, the GDY_F and GDY_O membranes can excellently separate CO2 and N-2 from CH4 in a wide temperature range. Moreover, the CO2/N-2 mixture can be effectively separated by GDY_O at temperatures lower than 300 K. Based on the kinetic theory, extremely high permeances were found for CO2 and N-2 passing through the GDY_X membranes (10(-4)-10(-2) mol/m(2) s Pa at 298 K). In addition, the influence of relative concentration on selectivity was also investigated for gases in the binary mixtures. This work provides an effective way to modify graphdiyne for the separation of large molecular gases, which is quite crucial in the gas separation industry. (C) 2017 Elsevier B.V.