The absorption power due to the electron-LO-phonon interaction in a cylindrical quantum wire (CQW) in the presence of a magnetic field is calculated. The dependence of absorption power on the photon energy is computationally calculated and graphically plotted for a specific CQW. From graphs of the absorption power, we determine cyclotron-resonance line-width (CRLW) as profiles of the curves. The numerical results show that the CRLW increases with increasing of the temperature and magnetic field, and CRLW decreases with increasing of the wire’s radius. The present results are in qualitative agreement with the existing theoretical and experimental results.