An intense electron beam travelling axially through the opening of a superconductor tube was studied. Model calculations showed that the beam is focused by the superconductor tube when the space-charge effect of the beam electrons is compensated. The tube functions as a lens for electrons injected parallel to the tube axis and also for electrons having a small initial radial velocity component. The electron trajectories were computed, and the focal length of the superconductor tube was estimated. (author). 2 figs., 6 refs.