Electrically stimulable nerve conduits are implants that could potentially be utilized in patients with nerve injury for restoring function and limb mobility. Such conduits need to be developed from specialized scaffolds that are both electrically conductive and allow neuronal attachment and differentiation. In this study, we investigate neural cell attachment and axonal differentiation on scaffolds co-woven with poly-(L-lactic acid) (PLLA) yarns and conducting threads. Yarns obtained from electrospun PLLA were co-woven with polypyrrole (PPy)-coated PLLA yarns or ultrathin wires of copper or platinum using a custom built low-resistance semi-automated weaving machine. The conducting threads were first electrically characterized and tested for stability in cell growth media. Suitability of the conducting threads was further assessed via cell viability studies using PC12 cells. Neurite growth was then quantified after electrically stimulating rat dorsal root ganglion (DRG) sensory neurons cultured on the woven scaffolds. Electrical conductivity tests and cellular viability studies demonstrated better bio-tolerability of platinum wires over PPy-coated PLLA yarns and copper wires. Electrically stimulated DRG neurons cultured on platinum-PLLA co-woven scaffolds showed enhanced neurite outgrowth and length. We demonstrate that a woven scaffold design could be utilized to incorporate conducting materials into cell-tolerable polymer yarns for developing electrically stimulable nerve conduits.