Direct transdifferentiation of somatic cells is a promising approach to obtain patient-specific cells for numerous applications. However, conversion across germ-layer borders often requires ectopic gene expression with unpredictable side effects. Here, we present a gene-free approach that allows efficient conversion of human fibroblasts via a transient progenitor stage into Schwann cells, the major glial cell type of peripheral nerves. Using a multikinase inhibitor, we transdifferentiated fibroblasts into transient neural precursors that were subsequently further differentiated into Schwann cells. The resulting induced Schwann cells (iSCs) expressed numerous Schwann cell-specific proteins and displayed neurosupportive and myelination capacity in vitro. Thus, we established a strategy to obtain mature Schwann cells from human postnatal fibroblasts under chemically defined conditions without the introduction of ectopic genes.