The spectral parameters of an electron in the multishell semiconductor cylindrical nanotube with a donor impurity at its axis have been studied in the framework of the effective mass and rectangular potential models, by using the modified Bethe variational method. The electronimpurity binding energies and the oscillator strengths of intra-band optical quantum transitions have been analyzed as functions of the geometrical parameters of a combined nanotube composed of semiconductors GaAs and Al0.4Ga0.6As. K e y w o r d s: semiconductor nanotube, donor impurity, binding energy, oscillator strength.