The first-principles total energy calculations with the local density approximation (LDA) and the plane wave pseudopotential method are employed to investigate the structural properties and electronic structures of Li3AlN2. The calculated lattice constants and inteal coordination of atoms agree well with the experimental results. Detailed studies of the electronic structure and the charge-density redistribution reveal the features of the strong ionicity bonding of Al-N and Al-Li, and strong hybridizations between Li and N in Li3AlN2. Our band structure calculation verifies Li3AlN2 is a direct gap semiconductor with the LDA gap value of about 2.97eV and transition at Γ.