Electrically conductive materials for the fabrication of scaffolds for neural tissue engineering purposes have attracted great attention. This is because electrical stimulation would improve neural cell growth, proliferation and differentiation. However appropriate mechanical properties and flexibility together with surface biocompatibility are required. In the present work attempts have been done to fabricate electrospun nanofibers based on a flexible thermoplastic urethane (TPU) and carbon nanotube as scaffold for neural regeneration with potential for electrical stimulation. Effects of the extent of electrical conductivities of TPU/CNT nanocomposites upon cell proliferation and cell differentiation have been investigated. Result revealed significant correlation between the electrical conductivity of the CNT dispersion state and behavior of the scaffold towards the seeded cells as well as differentiation towards the neural tissue. Correlation between the viscoelastic characteristics of the prepared TPU/CNT nanocomposites and cell signaling for the samples, before and after percolation threshold, have also been studied.