In the framework of density functional theory, using the plane-wave pseudopotential method, the nitrogen vacancy (VN) in both wurtzite and zinc-blende AlN is studied by the supercell approach. The atom configuration, density of states, and formation energies of various charge states are calculated. Two defect states are introduced by the defect,which are a doubly occupied single state above the valance band maximum (VBM) and a singly occupied triple state below the conduction band minimum (CBM) for wurtzite AlN and above the CBM for zinc-blende AlN. So VN acts as a deep donor in wurtzite AlN and a shallow donor in zinc-blende AlN. A thermodynamic transition level E(3+/+) with very low formation energy appears at 0.7 and 0.6eV above the VBM in wurtzite and zinc-blende structure respectively,which may have a wide shift to the low energy side if atoms surrounding the defect are not fully relaxed. Several other transition levels appear in the upper part of the bandgap. The number of these levels decreases with the structure relaxation. However, these levels are unimportant to AlN properties because of their high formation energy.