Human neural stem cells (NSCs) offer therapeutic potential for neurodegenerative diseases, such as inherited monogenic nervous system disorders, and neural injuries. Gene editing in NSCs (GE-NSCs) could enhance their therapeutic potential. We show that NSCs are amenable to gene targeting at multiple loci using Cas9 mRNA with synthetic chemically modified guide RNAs along with DNA donor templates. Transplantation of GE-NSC into oligodendrocyte mutant shiverer-immunodeficient mice showed that GE-NSCs migrate and differentiate into astrocytes, neurons, and myelin-producing oligodendrocytes, highlighting the fact that GE-NSCs retain their NSC characteristics of self-renewal and site-specific global migration and differentiation. To show the therapeutic potential of GE-NSCs, we generated GALC lysosomal enzyme overexpressing GE-NSCs that are able to cross-correct GALC enzyme activity through the mannose-6-phosphate receptor pathway. These GE-NSCs have the potential to be an investigational cell and gene therapy for a range of neurodegenerative disorders and injuries of the central nervous system, including lysosomal storage disorders.