Inherited demyelinating peripheral neuropathies are progressive incurable diseases without effective treatment. To develop a gene therapy approach targeting myelinating Schwann cells that can be translatable, we delivered a lentiviral vector using a single lumbar intrathecal injection and a myelin-specific promoter. The human gene of interest, GJB1, which is mutated in X-linked Charcot–Marie–Tooth Disease (CMT1X), was delivered intrathecally into adult Gjb1-null mice, a genetically authentic model of CMT1X that develops a demyelinating peripheral neuropathy. We obtained widespread, stable, and cell-specific expression of connexin32 in up to 50% of Schwann cells in multiple lumbar spinal roots and peripheral nerves. Behavioral and electrophysiological analysis revealed significantly improved motor performance, quadriceps muscle contractility, and sciatic nerve conduction velocities. Furthermore, treated mice exhibited reduced numbers of demyelinated and remyelinated fibers and fewer inflammatory cells in lumbar motor roots, as well as in the femoral motor and sciatic nerves. This study demonstrates that a single intrathecal lentiviral gene delivery can lead to Schwann cell-specific expression in spinal roots extending to multiple peripheral nerves. This clinically relevant approach improves the phenotype of an inherited neuropathy mouse model and provides proof of principle for treating inherited demyelinating neuropathies.