Possible geometrical structures and relative stabilities of (Li3N)n(n=1—5) clusters are studied by using the hybrid density functional theory(B3LYP) with 6-31G* basis sets. For the most stable isomers of (Li3N)n(n=1—5) clusters, the electronic structure, vibrational properties, bonds properties, ionization potentials are analyzed. The calculated results showed the following tendencies: the coordination number of N are usually 4 or 5; the bond lengths for the most of the optimized (Li3N)n(n=1—5) clusters are about 0.210—0.259nm for Li—Li and 0.185—0.204nm for the bridging Li—N bonds, while the terminal Li—N bonds span 0.172—0.178nm. The outcome of population analysis suggests that the natural charge of N atoms are about -2.01e and that of Li atoms are about +0.67e; the dynamic stabilities of Li3N and (Li3N)5 clusters are higher than that of other clusters.