Thin porous membranes with unidirectional oil-transport capacity offer great opportunities for intelligent manipulation of oil fluids and development of advanced membrane technologies. However, directional oil-transport membranes and their unique membrane properties have seldom been reported in research literature. Here, it is proven that a dual-layer nanofibrous membrane comprising a layer of superamphiphobic nanofibers and a layer of superhydrophobic oleophilic nanofibers has an unexpected directional oil-transport ability, but is highly superhydrophobic to liquid water. This novel fibrous membrane is prepared by a layered electrospinning technique using poly(vinylidene fluoride-hexafluoropropylene) (PVDF-HFP), PVDP-HFP containing well-dispersed FD-POSS (fluorinated decyl polyhedral oligomeric silsesquioxanes), and FAS (fluorinated alkyl silane) as materials. The directional oil-transport is selective only to oil fluids with a surface tension in the range of 23.8-34.0 mN m(-1). By using a mixture of diesel and water, it is further proven that this dual-layer nanofibrous membrane has a higher diesel-water separation ability than the single-layer nanofiber membranes. This novel nanofibrous membrane and the incredible oil-transport ability may lead to the development of intelligent membrane materials and advanced oil-water separation technologies for diverse applications in daily life and industry.