AlN and Al2N2 have been observed in the record of time-of-flight mass-spectra as positive ions. Associating with density functional theory(DFT) B3LYP method with 6-31G* basis set, we have carried out the optimizing calculations of the geometry, electronic state and vibrational frequency for (AlN)n (n = 1-15) clusters, moreover, discussed the character of the chemical bond and thermodynamical stability and explained the experimental mass spectra. The results show that there do not exist Al-Al and N-N bonds and only exists Al-N bond in the ground state structures of (AlN)n clusters; and the "magical number" regularity of (AlN)n is those whose atom number is 4, 8, 12, 16, 20, etc, all of which are times of four.