Nanofibrous membranes with superwetting performance have promising applications in oil adsorption or oil/water separation. However, the development of superwettable, stretchable and durable nanofiber composite for efficient separation of oil-in-water emulsion is still a challenge. Herein, a simple and versatile method was proposed to prepare flexible, superhydrophilic and electrically conductive polymer nanofiber composite with a core/shell structure by acidified carbon nanotubes (ACNTs) decoration onto polyurethane (PU) nanofibers and subsequent polydopamine (PDA) modification. Multiple interfacial hydrogen bonding among ACNTs, PDA and PU nanofibers results in the enhancement of both the tensile strength and Young's modulus of the PU nanofibrous membrane and also ensures the excellent stretchability, surface stability and durability of the nanofiber composite. The obtained superhydrophilic/underwater superoleophobic nanofiber composite exhibits superior anti-fouling property and can be used for high efficiency separation of oil-in-water (even corrosive) emulsion with outstanding recyclability. The flexible and multifunctional nanofiber composite with a unique PDA/ACNTs shell and polymer nanofiber core structure shows great potentials in practical oily wastewater purification.