We report the density- and size-controlled growth of zinc oxide (ZnO) nanorod arrays on arbitrary substrates using reduced graphene oxide (rGO) nanodot arrays. For the controlled growth of the ZnO nanorod arrays, rGO nanodot arrays with tunable density and size were designed using a monolayer of diblock copolymer micelles and oxygen plasma etching. While the diameter and number density of the ZnO nanorods were readily determined by those of the rGO nanodots, the length of the ZnO nanorods was easily controlled by changing the growth time. x-ray diffraction and electron microscopy confirmed that the vertically well-aligned ZnO nanorod arrays were heteroepitaxially grown on the rGO nanodots. Strong, sharp near-band-edge emission peaks with no carbon-related peak were observed in the photoluminescence spectra, implying that the ZnO nanostructures grown on the rGO nanodots were of high optical quality and without carbon contamination. Our approach provides a general and rational route for heteroepitaxial growth of high-quality inorganic materials with tunable number density, size, and spatial arrangement on arbitrary substrates using rGO nanodot arrays.