The electronic structures of InSb1−xNx nanowires are investigated using the ten-band k∙p method. It is found that nitrogen increases the Rashba coefficient of the nanowires dramatically. For thick nanowires, the Rashba coefficient may increase by more than 20 times. The semiconductor-metal transition occurs more easily in InSb1−xNx nanowires than in InSb nanowires. The electronic structure of InSb1−xNx nanowires is very different from that of the bulk material. For fixed x the bulk material is a semimetal, while the nanowires are metal-like. In InSb1−xNx bulk material and thick nanowires, an interesting decrease of electron effective mass is observed near k=0 which is induced by the nitrogen, but this phenomenon disappears in thin nanowires.