Innovative composites of biopolymers and nanomaterials have been exploited to fabricate wound dressings which show functional abilities to improve different stages of wound healing by a variety of mechanisms. In this study, a polymeric nanocomposite dressing is fabricated by electrospinning of a blend of sodium alginate (SA), poly vinyl alcohol (PVA) and graphene nanoplatelets (Gnp). The crosslinking of the nanofibers is done by thermal treatment followed by ionic bonding of the fibers. The crosslinked fibers are loaded by curcumin, a natural potent anti‐inflammatory compound, encapsulated in monomethoxy poly ethylene glycol‐oleate micelles/polymersomes (NCur). Results indicate that by incorporation of Gnp and NCur into the SA/PVA scaffold the tensile strength is not changed (~7 MPa) but the elongation to break and toughness of the scaffolds significantly increase from 11.25±2.6 and 50.56 to 35.5±5.1% and 125.9 Jm‐3, respectively. The scaffolds support the controlled release of curcumin for 24 h in vitro. Biocompatibility of the scaffolds has been confirmed by cell viability assay on mouse fibroblast cells. Overall, the findings demonstrate the potential applications of the spun fibers for wound dressing purposes.