Graphene-graft-polymer has been used to improve the compatibility between graphene and a polymer matrix, and to further enhance electrical, mechanical and biological properties of polymer/graphene composites. In this study, poly(trimethylene carbonate) (PTMC) was successfully grafted onto graphene surface via 'grafting from' method. Reduced graphene oxide (rGO) initiator was synthesized by azido ethanol reaction with graphene oxide (GO) at high temperature. This resulted in thermal reduction of the GO and stable hydroxyl groups on the graphene surface. Subsequently, rGO initiator was used for the ring-opening polymerization of TMC monomer. rGO-graft-PTMC composites with PTMC molecular weights of 430, 480, 2150 and 7030 g mol-1 were successfully synthesized using different amounts of TMC. Single layer graphene nanosheets remained after graft polymerization by this method. rGO-graft-PTMC dispersions in chloroform were stable. The rGO-graft-PTMC composites with PTMC molecular weights of 430-7030 g mol-1 had electrical conductivities ranging from 0.2 to 0.016 s cm-1. To investigate the biocompatibility of rGO-graft-PTMC, PTMC-based films containing rGO-graft-PTMC were prepared and used in cell culturing experiments. The composite films showed good biocompatibility with PC12 neuronal cells. It is concluded that rGO-graft-PTMC composite is a promising material for the preparation of nerve regeneration conduits.