We use first-principles calculation with pseudo-potential and plane wave method to study the electronic structure of LuI3. Exchange and correlation are treated in the local density approximation based on the density functional theory. The results show that the narrow bands with a width of about 0.2 eV near -4.4 eV are dominated by the 4f bands of Lu. Valence bands are located between -3.55 eV and 0 eV and mainly from p bands of I. Conduction bands are located between 2.44 eV and 12.35 eV and mainly from d bands of Lu, as well as from s bands of Lu. The peaks which appear at -3.46 eV of the s states of Lu, f states of Lu and p states of I show the strong interaction between the Lu and I.