Position- and morphology-controlled ZnO nanostructures are grown on an oxygen plasma-treated selective area of graphene layers using metal-organic vapor-phase epitaxy. The structural and optical characteristics examined by electron microscopy, cathodoluminescence and photoluminescence techniques indicate that high-quality nanostructures are prepared on graphene layers. This approach to grow the controlled ZnO nanostructures selectively on graphene layers enables us to fabricate various nanodevices including GaN/ZnO coaxial nanotube LED microarrays.