A freestanding membrane composed of a nanofiber network of a graphene-polymer nanocomposite is fabricated by electrospinning and applied as an optical element in fiber lasers. The functionalization of graphene with conjugated organic molecules provides a handle for improving mechanical and thermal properties as well as tuning the optical properties. A small loading (0.07 wt%) of functionalized graphene enhances the total optical absorption of poly(vinyl acetate) (PVAc) by 10 times. The electrospun graphene-polymer nanocomposites exhibit wideband saturable absorbance for laser pulse shaping, and attain a larger modulation depth and smaller nonsaturable loss than single-walled carbon nanotubes. The results show that electrospun graphene nanocomposites are promising candidtates as practical and efficient photonic materials for the generation of ultrashort pulses in fiber lasers.