Origins of the brain tumor, medulloblastoma, from stem cells or restricted progenitor cells are unclear. To investigate this, we activated oncogenic Hedgehog (Hh) signaling in multipotent and lineage-restricted CNS progenitors. We observed that normal unipotent cerebellar granule neuron precursors (CGNP) derive from hGFAP+ and Olig2+ RL progenitors. Hh activation in a spectrum of early and late stage CNS progenitors generated similar medulloblastomas, but not other brain cancers, indicating that acquisition of CGNP identity is essential for tumorigenesis. We show in human and mouse medulloblastoma that cells expressing the glia-associated markers Gfap and Olig2 are neoplastic and that they retain features of embryonic-type granule lineage progenitors. Thus, oncogenic Hh signaling promotes medulloblastoma from lineage-restricted granule cell progenitors.