GaN nanocolumns were synthesized on single-layer graphene via radio-frequency plasma-assisted molecular beam epitaxy, using a thin migration-enhanced epitaxy (MEE) AlN buffer layer as nucleation sites. Due to the weak nucleation on graphene, instead of an AlN thin-film we observe two distinguished AlN formations which affect the subsequent GaN nanocolumn growth: (i) AlN islands and (ii) AlN nanostructures grown along line defects (grain boundaries or wrinkles) of graphene. Structure (i) leads to the formation of vertical GaN nanocolumns regardless of the number of AlN MEE cycles, whereas (ii) can result in random orientation of the nanocolumns depending on the AlN morphology. Additionally, there is a limited amount of direct GaN nucleation on graphene, which induces nonvertical GaN nanocolumn growth. The GaN nanocolumn samples were characterized by means of scanning electron microscopy, transmission electron microscopy, high-resolution X-ray diffraction, room temperature micro-photoluminescence, and micro-Raman measurements. Surprisingly, the graphene with AlN buffer layer formed using less MEE cycles, thus resulting in lower AlN coverage, has a lower level of nitrogen plasma damage. The AlN buffer layer with lowest AlN coverage also provides the best result with respect to high-quality and vertically-aligned GaN nanocolumns. Recent progresses in the growth of GaN thin-film on graphene 1-6 increasingly justify the possibility for graphene to be a good alternative substrate over the available conventional substrates, for instance Si 7,8 , SiC 9 and sapphire 10. It is also reported that GaN thin-film is achievable on sapphire or amorphous substrates by employing either multi-layer or single-layer graphene as buffer layer 11-14. Such exploitations can be realized by taking advantage of the weak quasi-van der Waals binding 15-17 which can drastically relax the lattice matching condition to be satisfied by constituent materials. That being said, the lack of chemical reactivity of graphene and its extremely low surface energy 18 greatly disrupt the nucleation process of GaN, resulting in a low nucleation density 19 and difficulty in controlling the stacking sequence of the GaN growth 3. The latter issue, which often manifests in the form of stacking faults 3,5 or threading dislocations 1,4,17 , can possibly be suppressed by growing nanowire or nanocolumn structures 16,20-25. Nevertheless, because of the absence of dangling bonds in graphene, nanocolumns are often aligned in non-vertical directions 26-28 and/or have low density 27,29. Both problems are required to be addressed in order to demonstrate that the growth of III-N semiconductor nanostructures, particularly nanocolumns, utilizing graphene as the substrate can be further considered as an alternative platform in enabling the advancement of optoelectronic device performance and functionality, for instance light-emitting diodes 30. In this regard, the introduction of defects in graphene by means of plasma treatments could alleviate the issue of absence of dangling...