The geometrical and electronic structure of Al₂₄N₂₄ are optimized by using density functional theory (B3LYP) at the 6-31g(d) level. The results show that the geometrical structure symmetry of the optimized Al₂₄N₂₄ clusters are S₄, C₂, S₈, O. Based on the stable structure of the ground state, the transport property are obtained, the Al₂₄N₂₄ clusters are neither a p-type transport material, nor a n-type transport material, so, they have no transport properties. On the basis of the optimized ground state structure, the nuclear independent chemical shift values (NICS) of these isomers were studied, and the aromaticity were also studied. NICS values indicate that all isomers are aromatic and the characteristics of aromaticity are obtained.The IR-Raman spectra of the four clusters were obtained, and the order of vibrational intensity for the IR-Raman spectrums of the four clusters are S₈>S₄>C₂>O and S₈>S₄>O>C₂.