AlN was grown on 4H- or 6H-SiC (0001) on-axis substrates by plasma-assisted molecular beam epitaxy. By utilizing optimized SiC surface pretreatment, RHEED oscillations just after the growth of AlN were obtained with high reproducibility. This study focused on the growth kinetics of AlN and the correlation between kinetics and the crystalline quality of the grown layers. It was found that the growth mode changed from layer-by-layer to step-flow for high growth temperatures, while for lower temperatures the layer-by-layer growth mode persisted. The mechanism responsible for the change in growth mode is discussed. Symmetrical (0002) and asymmetrical (01–14) x-ray rocking curve measurements were carried out to evaluate the crystalline quality. For the (0002) peak, both high-temperature and low-temperature grown layers showed almost the same FWHM values. On the other hand, for the (01–14) peak, the FWHM of low-temperature grown AlN was much smaller (180 arcsec) than that of the high-temperature grown AlN (450 arcsec).