The energy spectra of carriers confined to a narrow gap semiconductor hollow cylinder with hard walls are calculated both without and with an applied constant axial magnetic field, taking into account the real band structure of InSb-type materials: narrow energy gap and strong spin-orbit interaction. We calculated the size and magnetic field dependence of effective g-value in bare InSb-type hollow cylinder for electrons. It has been seen that the effective g-value of the electrons decreases with increasing radius. The magnetic field dependence of g-factor has a minimum only for subbands with the negative in. (C) 2004 Elsevier B.V. All rights reserved.