The preparation and gas-separation performance of self-standing, high-flux, graphene oxide (GO) membranes is reported. Defect-free, 15-20 μm thick, mechanically stable, unsupported GO membranes exhibited outstanding gas-separation performance towards H /CO that far exceeded the corresponding 2008 Robeson upper bound. Remarkable separation efficiency of GO membranes for H and bulky C or C hydrocarbons was achieved with high flux and good selectivity at the same time. On the contrary, N and CH molecules, with larger kinetic diameter and simultaneously lower molecular weight, relative to that of CO , remained far from the corresponding H /N or H /CH upper bounds. Pore size distribution analysis revealed that the most abundant pores in GO material were those with an effective pore diameter of 4 nm; therefore, gas transport is not exclusively governed by size sieving and/or Knudsen diffusion, but in the case of CO was supplemented by specific interactions through 1) hydrogen bonding with carboxyl or hydroxyl functional groups and 2) the quadrupole moment. The self-standing GO membranes presented herein demonstrate a promising route towards the large-scale fabrication of high-flux, hydrogen-selective gas membranes intended for the separation of H /CO or H /alkanes.