Direct deposition of graphene on various dielectric substrates is demonstrated using a single-step chemical vapor deposition process. Single-layer graphene is formed through surface catalytic decomposition of hydrocarbon precursors on thin copper films predeposited on dielectric substrates. The copper films dewet and evaporate during or immediately after graphene growth, resulting in graphene deposition directly on the bare dielectric substrates. Scanning Raman mapping and spectroscopy, scanning electron microscopy, and atomic force microscopy confirm the presence of continuous graphene layers on tens of micrometer square metal-free areas. The revealed growth mechanism opens new opportunities for deposition of higher quality graphene films on dielectric materials.