We investigate the electronic properties of blue-phosphorene nanotubes using density functional theory first-principle calculations, taking into account, in particular, the presence of atom vacancies in the structure. The study considers both zigzag and armchair achiral configurations and reports on the structure and the electron energy states of the nanostructure. Compared to pristine blue-phosphorene nanotubes, which exhibit values of the fundamental bandgap between one and two electron-volts. For atomic single vacancies, the incorporation of spin-polarization helps to identify the induction of localized mid-gap states in the blue phosphorene nanotubes. The difference of energy between the highest near-valence and lower near-conduction localized states is, approximately, of 0.5 eV. Also the increase of the single vacancies concentration leads to the formation of additional bands that change the energy gap of the system.