It is highly desirable to reduce the membrane thickness in order to maximize the throughput and break the trade-off limitation for membrane-based gas separation. Two-dimensional membranes composed of atomic-thick graphene or graphene oxide nanosheets have gas transport pathways that are at least three orders of magnitude higher than the membrane thickness, leading to reduced gas permeation flux and impaired separation throughput. Here we present nm-thick molecular sieving membranes composed of porous two-dimensional metal-organic nanosheets. These membranes possess pore openings parallel to gas concentration gradient allowing high gas permeation flux and high selectivity, which are proven by both experiment and molecular dynamics simulation. Furthermore, the gas transport pathways of these membranes exhibit a reversed thermo-switchable feature, which is attributed to the molecular flexibility of the building metal-organic nanosheets.