Tissue Engineering (TE) is emerging as an effective way of curing different tissue oriented disorders and new tissue regeneration. Here, it has been attempted to show that biocompatible graphene oxide nanoplatelets (GOnPs)-polymer nanocomposites are novel materials for the fabrication of TE scaffolds for myoblast differentiation of human umbilical cord blood derived mesenchymal stem cells (CB-hMSCs). Addition of GOnPs in bioactive polymers like PCL (poly-caprolactone) and GO-PLGA (poly lactic co-glycolic acid) enhances electrical conductivity and biocompatibility of the electrospun composite scaffolds. CB-hMSCs were used for the direct differentiation to skeletal muscle cells (hSkMCs) on the electrospun GOnPs–PCL and GOnPs-PLGA nanocomposite scaffolds. These scaffolds exhibited admirable myoblast differentiation, proliferation and also promoted self-aligned myotubes formation. Moreover, IGF-1 cell signaling pathway study carried out on GOnPs-PCL composite scaffold meshes also showed their potentiality for excellent myoblast differentiation and proliferation. Structural, mechanical, microstructural and vibration spectroscopic studies were carried out to characterize the scaffold materials. Significantly enhanced values of both conductivity and dielectric constant provided favorable cues for the increase of cells-scaffold interaction and biocompatibility of GOnPs based polymer composite scaffolds. Present study confirmed GOnPs-polymer composite scaffolds as the potential candidates for the myoblast differentiation of CB-hMSCs for skeletal muscle or other tissues repair and regenerations.