Nuclear pore complexes (NPCs) act as effective and robust gateways between the nucleus and the cytoplasm, selecting for the passage of particular macromolecules across the nuclear envelope. NPCs comprise an elaborate scaffold that defines a approximately 30 nm diameter passageway connecting the nucleus and the cytoplasm. This scaffold anchors proteins termed 'phenylalanine-glycine' (FG)-nucleoporins, the natively disordered domains of which line the passageway and extend into its lumen. Passive diffusion through this lined passageway is hindered in a size-dependent manner. However, transport factors and their cargo-bound complexes overcome this restriction by transient binding to the FG-nucleoporins. To test whether a simple passageway and a lining of transport-factor-binding FG-nucleoporins are sufficient for selective transport, we designed a functionalized membrane that incorporates just these two elements. Here we demonstrate that this membrane functions as a nanoselective filter, efficiently passing transport factors and transport-factor-cargo complexes that specifically bind FG-nucleoporins, while significantly inhibiting the passage of proteins that do not. This inhibition is greatly enhanced when transport factor is present. Determinants of selectivity include the passageway diameter, the length of the nanopore region coated with FG-nucleoporins, the binding strength to FG-nucleoporins, and the antagonistic effect of transport factors on the passage of proteins that do not specifically bind FG-nucleoporins. We show that this artificial system faithfully reproduces key features of trafficking through the NPC, including transport-factor-mediated cargo import.