Using van der Waals corrected density functional theory (DFT), we theoretically predict the performance of a strain-controlled graphenylene membrane in multifunctional gas separation. By applying lateral strain to this membrane, we find that the transition points between “closed” and “open” states for CO2, N2, CO, and CH4 passing through graphenylene membrane occur under 3.04%, 4.20%, 5.12%, and 10.78% strain, respectively. The H2 permeance is remarkably enhanced through tensile strain, and it reaches 2.6 × 10−2 mol s−1 m−2 Pa−1 under 3.04% strain, which is about 6 times higher than that with unstrained graphenylene membrane. At strain levels between 3.04% and 4.20%, this membrane can be used to separate CO2/N2. In particular, at strain levels of 4.20%, the permeance of CO2 for this strained membrane can reach 1.03 × 10−7 mol s−1 m−2 Pa−1 as well as 15.4 selectivity for CO2/N2, which are both higher than the industrially acceptable values of the permeance and selectivity. In addition, with a strain magnitude from 5.12% to 10.78%, a graphenylene monolayer can be used as a CH4 upgrading membrane. Our results demonstrate the promise of a tunable, multifunctional graphenylene gas-separation membrane, wherein the sizes of the nanopores can be precisely regulated by tensile strain. These findings may be useful for designing tunable nanodevices for gas separation and other applications.