One of the best methods to prevent wound infection and speed up wound healing is wound dressing based on nanofiber–polymer scaffolds, which have acceptable antimicrobial performance and appropriate skin regeneration capabilities. In this paper, the electrospinning method was applied to synthesize the polyvinylpyrrolidone-acrylic acid hydrogel (PVPA)–eggshell membrane (ESM)–reduced graphene oxide (rGO) nanosheets nanocomposite dressings with different reduced graphene oxide contents (0, 0.5, 1, and 2 wt.%). Thus, smooth nanofibers were fabricated, including a high amount of rGO, which reduced the fiber diameter. Based on the results, rGO played an important role in water impermeability. The results showed that by increasing the rGO concentration from 0.5 to 2 wt%, the contact angle value increased persistently. Results showed that compared to PVPA–ESM, the mechanical strength and strain of PVPA–ESM/1 wt% rGO significantly enhanced 28% and 23%, respectively. Incorporation of 1 wt% rGO enhanced swelling ratio from 875% for PVPA-ESM to 1235% after 420 min, while increasing the rGO to 2 wt% increased the degradation rate of the composites. According to the in vitro cell culture studies, PVPA-ESM wound dressings with 0.5–1 wt% rGO content enhanced PC12 cell viability compared to the wound dressings without rGO nanosheets. Generally, rGO–loaded PVPA-ESM nanofiber wound dressing can be considered as a potential candidate to be used in skin regeneration applications.