We have grown AlN nanorods and AlN films using plasma-assisted molecular beam epitaxy by changing the Al source flux. Plasma-assisted molecular beam epitaxy of AlN was performed on c-plane Al2O3 substrates with different levels of aluminum (Al) flux but with the same nitrogen flux. Growth behavior of AlN was strongly affected by Al flux, as determined by in-situ reflection high energy electron diffraction. Prior to the growth, nitridation of the Al2O3 substrate was performed and a two-dimensionally grown AlN layer was formed by the nitridation process, in which the epitaxial relationship was determined to be [11-20]AlN//[10-10]Al2O3, and [10-10]AlN//[11-20]Al2O3. In the growth of AlN films after nitridation, vertically aligned nanorod-structured AlN was grown with a growth rate of 1.6μm/h, in which the growth direction was<0001>, for low Al flux. However, with high Al flux, Al droplets with diameters of about 8μm were found, which implies an Al-rich growth environment. With moderate Al flux conditions, epitaxial AlN films were grown. Growth was maintained in two-dimensional or three-dimensional growth mode depending on the Al flux during the growth; however, final growth occurred in three-dimensional growth mode. A lowest root mean square roughness of 0.6 nm (for 2μm×2μm area) was obtained, which indicates a very flat surface.