Nanoporous graphene membrane (NGM) has enormous potential and excellent properties in practical applications. But almost all of the previous studies were based on the assumption that the nanopores were symmetric along the normal vector of the graphene plane. Asymmetric nanoporous graphene membrane (A-NGM), a promising membrane material in energy, environment and bionic, was seldom researched until now. A kind of graphene membrane with asymmetric semisphere nanopore embedded in it is designed. Such a membrane is provided with the properties of A-NGM. Its electron properties and van der Waals surface are analyzed by quantum chemistry approach. Permeation mechanism of helium, neon and argon across this graphene membrane is analyzed by employing Langmuir adsorption isotherm. Molecular dynamics simulations are used to characterize the asymmetric performance of A-NGM for gas permeance. The driving force of these dynamical processes is revealed by implementing noncovalent interaction analysis. These results are considered not only assist in the designing of asymmetric membrane material, but also pave the way toward the realization of unidirectional graphene membrane in the future.