Spinal cord neural stem cells (NSCs) have great potential to reconstitute damaged spinal neural circuitry, but they have yet to be generated in vitro. We now report the derivation of spinal cord NSCs from human pluripotent stem cells (hPSCs). Our observations show that these spinal cord NSCs differentiate into a diverse population of spinal cord neurons occupying multiple positions along the dorso-ventral axis, and can be maintained for prolonged time periods. Grafts into injured spinal cords were rich with excitatory neurons, extended large numbers of axons over long distances, innervated their target structures, and enabled robust corticospinal regeneration. The grafts synaptically integrated into multiple host intraspinal and supraspinal systems, including the corticospinal projection, and improved functional outcomes after injury. hPSC-derived spinal cord NSCs could enable a broad range of biomedical applications for in vitro disease modeling and constitute an improved clinically translatable cell source for 'replacement' strategies in several spinal cord disorders.