The recovery of impaired peripheral nerves is often not as expected, which makes the development of nerve conduits trendy nowadays. To enable the neural messages effectively being delivered as well as to prevent the secondary damage during the removal of nerve conduits, the conductivity and biodegradability are two essential requirements for ideal nerve conduits. In this study, electrospinning is used to produce polyvinyl alcohol (PVA)/carbon nanotubes (CNT) electrospun films, after which the morphology analysis, electrical property, water contact angle, and biological characteristics of the membranes are investigated, thereby determining the optimal nerve conduits based on the employment of electrospinning, PVA, and CNT. The test results indicate that with 0.25 wt% of PVA, the electrospun films exhibit comparatively lower resistance of 25.3 ohm, good fibrous morphology with a diameter being 1 μm. In addition, the electrospun films are cytotoxicity-free and facilitate the growth of cells. It is observed in the MMT assay that after co-cultured with cells for three days, PVA/CNT electrospinning fibrous membranes exhibit a cellular viability that is 18.5 times greater than that of the control group on Day 1. According to all property evaluations, PVA/CNT electrospinning fibrous membranes are a qualified candidate for the use of nervous conduits.