Graphene is a distinct two-dimensional material that offers a wide range of opportunities for membrane applications because of ultimate thinness, flexibility, chemical stability, and mechanical strength. We demonstrate that few- and several-layered graphene and graphene oxide (GO) sheets can be engineered to exhibit the desired gas separation characteristics. Selective gas diffusion can be achieved by controlling gas flow channels and pores via different stacking methods. For layered (3- to 10-nanometer) GO membranes, tunable gas transport behavior was strongly dependent on the degree of interlocking within the GO stacking structure. High carbon dioxide/nitrogen selectivity was achieved by well-interlocked GO membranes in high relative humidity, which is most suitable for postcombustion carbon dioxide capture processes, including a humidified feed stream.