Abstarct: BN nanotubes have various functions in various industries, due to high temperature and chemical stability and resistance in oxidation. In this work, the stability, electronic and structure properties of pure and doped double-walled BN nanotubes with C atom were studied baxsed on density functional theory using the generalized gradient approximation (GGA) with SIESTA code. The calculations have been done on armchair (5,5)@(n,n) and (6,6)@(n,n) with (n=7-15) and zigzag (6,0)@(n,0) and (7,0)@(n,0) with (n=10-18) pure double-walled BN nanotubes. The results of the stability study of pure double-walled nanotubes shows that the armcheir pure double walled BN nanotubes with difference chirality 6, (n,n)@(n+6,n+6) and inter-wall space 4.2 Å and the zigzag nanotubes with difference chirality 9, (n,0)@(n+9,0) and inter-wall space 3.6 Å are the most stable structures. Studying the band structure shows that all pure armchair and zigzag nanotubes are semiconductor. Band gap of the Single-walled BN nanotubes are 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 BN nanotubes are less than the its constituent Single-walled nanotubes. Armchair (5,5)@(7,7), (5,5)@(9,9), (5,5)@10,10), (6,6)@(8,8), (6,6)@(10,10) and (6,6)@(11,11) and zigzag (6,0)@(10,0), (6,0)@(11,0), (6,0)@(12,0), (7,0)@(12,0), (7,0)@13,0) and (7,0)@(14,0) double-walled BN nanotubes were doped with C atom. The results of the doped armchair and zigzag double-walled nanotubes reflects the reduction in inter-wall space compared to pure mode and is also the phase change from insulating to conducting. The results of this research can be useful application for the experiment studies in future. According to the results of this research, the BN nanotube suggested as a proper candidate for produce composite materials and application in electronic industries.