We report a three-step method to grow high-quality AlN heteroepitaxial layers on sapphire substrates at relatively low temperatures by metalorganic chemical vapor deposition (MOCVD) without the use of epitaxial lateral overgrowth (ELO) or pulse atomic layer epitaxy (PALE) method. The three-layer AlN structure comprises a 15-nm thick buffer layer, a 50-nm thick intermediate layer, and a 3.4-μm thick template layer grown at 930, 1130, and 1100°C sequentially on the c-plane sapphire substrate. The resulting AlN layer had smooth surface with well-defined terraces and low root-mean square (RMS) roughnesses of 0.50 and 0.07nm for 20×20 and 1×1μm2 atomic force microscopy (AFM) scans. Band-edge emission was observed at 208nm by room temperature (RT) photoluminescence (PL) measurements. The total threading dislocation density was 2.5×109/cm2 as determined by transmission electron microscopy (TEM), which is comparable to those of some AlN layers recently grown at significantly higher temperatures. Growth evolution was studied and correlated to the TEM results. The residual impurity concentrations were comparable to those of AlN layers grown at higher temperatures, i.e., 1200-1600°C. This study demonstrates the high quality AlN layers on sapphire substrates can be grown at achievable temperatures for most of the modern MOCVD systems.