Novel membrane materials for H₂ separation are wanted. How to overcome the “trade-off” between membrane permeability and selectivity is a tough challenge. Here we report new random organic framework membranes with benzimidazole and imine linkages to form hierarchical channels. Both high H₂-selective and fast H₂ transport pathways are created. The preparation parameters are thoroughly studied and the membrane structures are well characterized by SEM, AFM, NMR, XPS, gas sorption, etc. Effect of feed conditions on membrane performance, such as composition, pressure and temperature, is investigated. The membrane performance transcends the upper bounds of H₂/CO₂, H₂/N₂ and H₂/CH₄ with excellent stability.