We present a systematic theoretical investigation of gas permeability through single-layer nanoporous graphene membranes with N-terminated (pyridinic and mixed pyridinic/pyrrolic) pores for He, H2, N2, O2, CO, CO2, H2O, and CH4. Our study is based on density functional theory transition-state calculations and the kinetic theory of gasses. We systematically evaluate pores of varying sizes and shapes up to 5.7 Å in diameter. According to our findings, membranes with pores in the size regime (4.5 Å - 5.0 Å) may exhibit industrially acceptable permeance to several gas molecules and advanced selectivity. Notably, we found that, among a few others, a pore with the same topological features at the pore boundary as those of the characteristic pore of g-C3N4 carbon nitride, is particularly promising. In addition, membranes with larger pores, ∼5.5 Å - 5.7 Å, can effectively separate CH4 from the other molecules. Our findings support the advanced potential of single-layer graphene membranes with nitrogen-terminated sub-nanometer pores, for gas separation applications.