A superhydrophobic fibrous membrane (FM), which consists of elastic polyurethane (PU) and chromatic polydiacetylenes (PDA), is fabricated using an electrospinning technique, followed by short-time UV irradiation and heating treatment. The FM with fine hierarchical roughness exhibits excellent superhydrophobicity and breathability under even 300% strain of biaxial stretching. It can effectively separate the oil-sea water mixture, solely using gravity, with fascinating permeate flux (6369.4 +/- 37.7 L m(-2) h(-1)), high separation efficiency, excellent recyclability and stability against corrosive liquids. Furthermore, the FM shows good air permeability and mechanical properties. Our design starts from simple chemistry, and may offer a versatile and scalable approach to fabricate hierarchically structured superhydrophobic FMs for variously potential applications, including the cleanup of oil spills, waste water treatment, packaging of stretchable electronics and protective clothing.