Abstarct: AlN nanotubes have attract much attention due to their significant properties such as high temperature stability and high melting point, considerable thermal conductivity and low thermal expansion. In this work, the stability, electronic and structure properties of pure and doped and capsulated double-walled AlN nanotubes with Ga atom were studied baxsed on density functional theory by considering wander vals forces with SIESTA code. The calculations have been done on armchair (5,5)@(n,n) with (n=8-15) and (6,6)@(n,n) with (n=9-16) and zigzag (6,0)@(n,0) with (n=12-19) and (5,0)@(n,0) with (n=11-18) double-walled AlN nanotubes. The results of the stability study of pure double-walled nanotubes shows that the armchair double walled AlN nanotubes with difference chirality of 7, (n,n)@(n+7,n+7) and inter-wall distance of 6 Å and the zigzag nanotubes with difference chirality of 12, (n,0)@(n+12,0) and inter-wall distance of 6.06 Å are the most stable structures. Studying the band structure shows that all pure zigzag nanotubes are semiconductor with direct band gap and all pure armchair nanotubes are semiconductor with indirect band gap. Band gap of the Single-walled AlN nanotubes have increasing trend with increasing the diameter of the nanotubes and the process of change is slower in the higher diameters. The band gap of double-wall AlN nanotubes are less than it’s constituent single-walled nanotubes. Armchair and zigzag double-walled AlN nanotubes were doped with Ga atoms. The results of the doped armchair and zigzag double-walled nanotubes indicate a reduction in band gap of the nanotubes compared to pure mode.It was observed That by encapsulating The nanotubes, The interwall distances and The nanotube Stubility increased. The results of this research can be useful for the experiment studies in future.