GaN epilayers are globally grown on amorphous glass substrates via a compound buffer layer including Ti preorienting layer and AlN nucleation layer (NL) grown by molecular beam epitaxy at 530 degrees C. It is shown that the ratio of V/III during AlN growth plays a key role in the crystallinity of AlN NL as a trade-off between the formation of Al clusters and the mobility of Al adatoms. The N-2 flux has an optimal value of 2.4 sccm when the Al flux is fixed to 7.46 x 10(-8) Torr at the RF power of 400 W. The obtained smooth GaN epilayer is hexagonal single-crystalline with the grain size in the order of submicron magnitude and root-mean-square roughness of 2.83 nm, which shows the great potential in the epitaxy of III-nitrides on amorphous glass substrates.