Semiconductor nanowire arrays integrated vertically on graphene films offer significant advantages for many sophisticated device applications. We report on van der Waals (VDW) epitaxy of InAs nanowires vertically aligned on graphene substrates using metal-organic chemical vapor deposition. The strong correlation between the growth direction of InAs nanowires and surface roughness of graphene substrates was investigated using various graphene films with different numbers of stacked layers. Notably, vertically well-aligned InAs nanowire arrays were obtained easily on single-layer graphene substrates with sufficiently strong VDW attraction. This study presents a considerable advance toward the VDW heteroepitaxy of inorganic nanostructures on chemical vapor-deposited large-area graphenes. More importantly, this work demonstrates the thinnest epitaxial substrate material that yields vertical nanowire arrays by the VDW epitaxy method.