Electrically conductive hyaluronic acid (HA) hydrogels incorporated with single-walled carbon nanotubes (CNTs) and/or polypyrrole (PPy) were developed to promote differentiation of human neural stem/progenitor cells (hNSPCs). The CNT and PPy nanocomposites, which do not easily disperse in aqueous phases, dispersed well and were efficiently incorporated into catechol-functionalized HA (HA–CA) hydrogels by the oxidative catechol chemistry used for hydrogel cross-linking. The prepared electroconductive HA hydrogels provided dynamic, electrically conductive three-dimensional (3D) extracellular matrix environments that were biocompatible with hNSPCs. The HA–CA hydrogels containing CNT and/or PPy significantly promoted neuronal differentiation of human fetal neural stem cells (hfNSCs) and human induced pluripotent stem cell-derived neural progenitor cells (hiPSC-NPCs) with improved electrophysiological functionality when compared to differentiation of these cells in a bare HA–CA hydrogel without electroconductive motifs. Calcium channel expression was upregulated, depolarization was activated, and intracellular calcium influx was increased in hNSPCs that were differentiated in 3D electroconductive HA–CA hydrogels; these data suggest a potential mechanism for stem cell neurogenesis. Overall, our bioinspired, electroconductive HA hydrogels provide a promising cell-culture platform and tissue-engineering scaffold to improve neuronal regeneration.