The electronic structures of Al3Y in the three (DO19, Ll2, and DO22) phases were investigated using the allelectron total energy self-consistent LMTO method. The calculated results for total energy showed that the hexagonal DO19 phase is the most stable structure among these three phases, this is in agreement with experiment. Furthermore, it is found that the stability depends strongly upon the band filling of the bonding states and exhibits a inverse relationship with the density of states at EF.