Chemical, petrochemical, energy, and environment-related industries strongly require high-performance nanofiltration membranes applicable to organic solvents. To achieve high solvent permeability, filtration membranes must be as thin as possible, while retaining mechanical strength and solvent resistance. Here, we report on the preparation of ultrathin free-standing amorphous carbon membranes with Young's moduli of 90 to 170 gigapascals. The membranes can separate organic dyes at a rate three orders of magnitude greater than that of commercially available membranes. Permeation experiments revealed that the hard carbon layer has hydrophobic pores of ~1 nanometer, which allow the ultrafast viscous permeation of organic solvents through the membrane.