Electrospinning of composite polymer solutions provides fantastic potential to prepare novel nanofibers for use in a variety of applications. The addition of graphene (G) and graphene oxide (GO) nanosheets to bioactive polymers was found to enhance their conductivity and biocompatibility. Composite conductive nanofibers of polyaniline (PANI) and polyacrylonitrile (PAN) with G and GO nanosheets were prepared by an electrospinning process. The fabricated membranes were investigated by physical and chemical examinations including scanning electron microscopy (SEM), Raman spectroscopy, x-ray diffraction (XRD) and tensile assay. The muscle satellite cells enriched by a pre-plating technique were cultured in the following and their proliferation and differentiation behavior studied by MTT, Real-Time PCR assays and 4', 6-diamidino-2-phenylindole (DAPI) staining. The cultured cells on composite nanofibrous PAN/PANI-CSA/G confirmed a higher proliferation and differentiation value compared to other groups including PAN/PANI-CSA/GO and PAN/PANI-CSA scaffolds. Furthermore, the higher stiffness of the former scaffold showed a lower cell spreading as a function of stem cell activation into more proliferative cells. It is supposed that the enhanced conductivity value in addition to relative higher stiffness of the PAN/PANI-CSA/G composite nanofibers plays a favorable role for proliferation and differentiation of satellite cells.