By restricting the periodic boundary condition of wave vector , the model of toroidal carbon nanoscrolls in a magnetic field is constructed on the basis of graphene tight-binding model, and its electronic structure properties are studied. The results show that the electronic structure with the magnetic flux Φ0 changes periodically with the magnetic flux Φ, which can be modulated into a metal or a bandgap semiconductor by controlling the chirality and magnetic field. The bandgap of zigzag toroidal carbon nanoscrolls with m = 3I (I is integer) is less affected by magnetic field, and the variation is only 7 μeV at m =18.
