We report a three-step growth method to grow thick and high quality aluminum nitride (AlN) epilayers on sapphire substrates by metal organic chemical vapor deposition (MOCVD). The three-step growth method begins with a deposition of a thin AlN buffer layer at 950 °C followed by an intermediate AlN (I-AlN) layer at 1100 °C, and finally a thick AlN epilayer at high temperature around 1325 °C. AlN epilayers grown by this method have smooth surfaces, narrow width of X-ray rocking curves, and strong band edge photoluminescence (PL) emissions with low impurity emissions. Transmission electron microscopy revealed that most of the threading dislocations are annihilated within 300 nm. Stacking faults are greatly reduced in epilayers grown by this method resulting in very low screw type threading dislocation density. Dominant threading dislocations in the AlN epilayers are edge type originated from misfit dislocations (MD).