Uniform core-sheath nanofibers are prepared by electrospinning a water-in-oil emulsion in which the aqueous phase consists of a poly(ethylene oxide) (PEO) solution in water and the oily phase is a chloroform solution of an amphiphilic poly(ethylene glycol)-poly(L-lactic acid) (PEGPLA) diblock copolymer. The obtained fibers are composed of a PEO core and a PEG-PLA sheath with a sharp boundary in between. By adjusting the emulsion composition and the emulsification parameters, the overall fiber size and the relative diameters of the core and the sheath can be changed. A mechanism is proposed to explain the process of transformation from the emulsion to the core-sheath fibers, i.e., the stretching and evaporation induced de-emulsification. In principle, this process can be applied to other systems to prepare core-sheath fibers in place of concentric electrospinning and it is especially suitable for fabricating composite nanofibers that contain water-soluble drugs.