The interconnected porous structures that mimic the extracellular matrix support cell growth in tissue engineering. Nanofibers generated by electrospinning can act as a vehicle for therapeutic cell delivery to a neural lesion. The incorporation of carbon nanomaterials with excellent electrical conductivity in nanofibers is an attractive aspect for design of a nanodevice for neural tissue regeneration. In this study, nanoscaffolds were created by electrospinning poly(ϵ-caprolactone) (PCL) and three different types of carbon nanomaterials, which are carbon nanotubes, graphene, and fullerene. The component of carbon nanomaterials in nanofibers was confirmed by Fourier transform infrared spectroscopy. The fiber diameter was determined by scanning electron microscopy, and it was found that the diameter varied depending on the type of nanomaterial in the fibers. The incorporation of carbon nanotubes and graphene in the PCL fibers increased the contact angle significantly, while the incorporation of fullerene reduced the contact angle significantly. Incorporation of CNT, fullerene, and graphene in the PCL fibers increased dielectric constant. Astrocytes isolated from neonatal rats were cultured on PCL-nanomaterial nanofibers. The cell viability assay showed that the PCL-nanomaterial nanofibers were not toxic to the cultured astrocytes. The immunolabeling showed the growth and morphology of astrocytes on nanofiber scaffolds. SEM was performed to determine the cell attachment and interaction with the nanoscaffolds. This study indicates that PCL nanofibers containing nanomaterials are biocompatible and could be used for cell and drug delivery into the nervous system.