Porous fibrous membranes having multiple scales geometries and tailored properties have become attractive microfabrication materials in recent years. Due to the feasibility of incorporating graphene in electrospun nanofibres and the growing interest on these nanomaterials, the present paper focuses on the electrospinning of Poly (ε-Caprolactone) (PCL) solutions in the presence of different amounts of Graphene platelets. Electrospinning is a process whereby ultrafine fibers are formed in a high-voltage electrostatic field. The morphological appearance, fiber diameter, and structure of PCL nanofibers produced by the electrospinning process were studied in the presence of different concentration of graphene. Moreover, the effect of a successful incorporation of graphene nanosheets into PCL polymer nanofibers was analyzed. Scanning electron microscope micrographs of the electrospun fibers showed that the average fiber diameter increases in the presence of graphene. Furthermore, the intrinsic properties developed due to the interactions of graphene and PCL improved the mechanical properties of the nanofibers. The results reveal the effect of various graphene concentrations on PCL and the strong interfacial interactions between the graphene platelets phase and the polymer matrix. The functional complexity of the electrospun fibers provides significant advantages over other techniques and shows the promise of these fibers for many applications including air/water filters, sensors, organic solar cells, smart textiles, biocompatible scaffolds for tissue engineering and load-bearing applications. Optimizing deposition efficiency, however, is a necessary milestone for the widespread use of this technique.