Conductive biomaterials have recently gained much attention, specifically owing to their application for electrical stimulation of electrically excitable cells. Herein, flexible, electrically conducting, robust fibers composed of both an alginate biopolymer and graphene components have been produced using a wet-spinning process. These nanocomposite fibers showed better mechanical, electrical, and electrochemical properties than did single fibers that were made solely from alginate. Furthermore, with the aim of evaluating the response of biological entities to these novel nanocomposite biofibers, in vitro studies were carried out using C2C12 myoblast cell lines. The obtained results from in vitro studies indicated that the developed electrically conducting biofibers are biocompatible to living cells. The developed hybrid conductive biofibers are likely to find applications as 3D scaffolding materials for tissue engineering applications.