The excellent thermal and chemical stability of monolayer graphene makes it an ideal material for separations at high temperatures and in harsh organic solvents. Here, based on understanding of solvent permeation through nanoporous graphene via molecular dynamics simulation, a resistance model was established to guide the design of a defect-tolerant graphene composite membrane consisting of monolayer graphene on a porous supporting substrate. Guided by the model, we experimentally engineered polyimide (PI) supporting substrates with appropriate pore size, permeance, and excellent solvent resistance and investigated transport across the resulting graphene-covered membranes. The cross-linked PI substrate could effectively mitigate the impacts of leakage through defects across graphene to allow selective transport without defect sealing. The graphene-covered membrane showed pure solvent permeance of 24.1 L m h bar and stable rejection (∼90%) of Allura Red AC (496.42 g mol ) in a harsh polar solvent, dimethylformamide (DMF), at 100 °C for 10 d.