The stability and electronic structures of AlN nanowires with and without N-vacancy are investigated using firstprinciples calculations.We find that there is an inverse correlation between formation energy and diameter in ideal A1N nanowires.After calculating the formation energies of N-vacancy at different sites in AlN nanowires with different diameters,we find that the N-vacancy prefers to stay at the surface of the nanowires and it is easier to fabricate them under Al-rich conditions.Through studying the electronic properties of A1N nanowires with N-vacancies,we further find that there are two isolated bands in the deep part of the band gap,one of them is fully occupied and the other is half occupied.The charge density indicates that the half-fully occupied band arises from the A1 at the surface,and this atom becomes an active centre.