Superconductor Nb open nanotubes are analyzed under a strong transport current in an external magnetic field using the time-dependent Ginzburg–Landau equations. The geometric properties of the hysteresis loop in current–voltage characteristics are described for nanotubes of different radii from 190 to 440 nm as a function of the magnetic field. The hysteresis effect appears at a constant temperature as a result of the order parameter dynamics. In nanotubes of radii equal to 240 nm and larger, the area of the hysteresis loop manifests a non-monotonic behavior as a function of the external magnetic field with a maximum ranging from 15 to 20 mT. Normal conductivity is shown to have a crucial impact on the hysteresis effect in superconductor open nanotubes. Namely, a higher normal conductivity leads to the disappearance of the hysteresis effect. As a rule, the upper and lower branches of the hysteresis loop are provided by the phase-slip and vortex regimes, correspondingly. Just before the transition of the system from the upper branch to the lower one, the way of nucleation and annihilation of vortices in the region with suppressed superconductivity experiences readjustment.