Healing of nerve injuries is a critical medical issue. Biodegradable polymeric conduits are a promising therapeutic solution to provide guidance for axon growth in a given space, thus helping nerve heal. Extensive studies in the past decade reported that conductive materials could effectively increase neurite and axon extension in vitro and nerve regeneration in vivo. In this study, graphene oxide and carbon nanotubes were covalently functionalized with double bonds to obtain crosslinkable graphene oxide acrylate (GOa) sheets and carbon nanotube poly(ethylene glycol) acrylate (CNTpega). An electrically conductive reduced GOa-CNTpega-oligo(polyethylene glycol fumarate) (OPF) hydrogel (rGOa-CNTpega-OPF) was successfully fabricated by chemically crosslinking GOa sheets and CNTpega with OPF chains followed by in situ chemical reduction in l-ascorbic acid solution. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) imaging showed homogenous distribution of GOa/CNTpega carbon content in the rGOa-CNTpega-OPF composite hydrogel, resulting in a significant increase of electrical conductivity compared with neutral OPF without carbon content. Cell studies showed excellent biocompatibility and distinguished PC12 cell proliferation and spreading on the rGOa-CNTpega-OPF composite hydrogel. Fluorescent microscopy imaging demonstrated robustly stimulated neurite development in these cells on a conductive rGOa-CNTpega-OPF composite hydrogel compared with that on neutral OPF hydrogels. These results illustrated a promising potential for the rGOa-CNTpega-OPF composite hydrogel to serve as conduits for neural tissue engineering.