Graphene-based materials have been used for fabricating organic solvent nanofiltration membranes due to their excellent mechanical properties and chemical stability in organic solvents. However, graphene membranes exhibit low organic solvent permeation properties due to the large molecular size of the organic solvent molecules and their strong interactions with the graphene surface. Herein, a nanoporous graphene membrane was fabricated to enhance organic solvent permeation. Nanopores were generated on the basal plane of graphene by rapid thermal annealing of graphene oxide. The size of the nanopores was also tuned from micropores to nanopores by adjusting the activation temperatures. The optimized nanoporous graphene membrane showed ultrafast isopropyl alcohol permeance up to 295 Lm−2h−1bar−1 and a sharp molecular weight cut-off of 616 Da. The membrane showed excellent stability and diafiltration performance under cross-flow filtration with a separation factor of around 1000 for dye molecules mixed in isopropyl alcohol.