Porous graphene (PG) and nitrogen-substituted PG monolayers of 3N-PG and 6N-PG were designed as effective membranes for the separation of He and H-2 over Ne, Ar, N-2, CO, and CH4 by using density functional theory. Results showed that PG and 3N-PG exhibited suitable pore sizes and relatively high stabilities for He and H-2 separation. PG and 3N-PG membranes also presented excellent He and H-2 selectivities over Ne, Ar, N-2, CO and CH4 at a wide temperature range. 6N-PG membrane exerted unexceptionable permeances of the studied gases, especially He and H-2, which could remarkably improve the separation efficiency of He and H-2. Analyses on the most stable adsorption configurations and maximum adsorption energies indicated weak Van der Waals interactions between the gases and the three PG based membranes. Microscopic permeation process analyses based on the minimum energy pathway, energy profiles, and electron density isosurfaces elucidated the remarkable selectivities of He over Ne/CO/N-2/Ar/CH4 and H-2 over CO/N-2/CH4 and the high permeances of He and H-2 passing through the three PG-based membranes. This work not only highlighted the potential use of the three PG-based membranes for He separation and H-2 purification but also provided a superior alternative strategy to design and screen membrane materials for gas separation. (C) 2018 Elsevier B.V. All rights reserved.