Phonon-assisted cyclotron resonance (PACR) in cylindrical quantum wire (CQW) is investigated via multiphoton absorption process when electrons are scattered by LO-phonon. The additional peaks in the absorption spectrum due to transitions between Landau levels accompanied by emission and absorption of LO-phonon are indicated. From curves on graphs of the absorption power, we obtain PACR-linewidth as profiles of the curves by using profile method. The temperature and magnetic field dependence of the absorption power and PACR-linewidth are investigated. The results are compared with those in the monophoton absorption. The calculations demonstrate that the multiphoton absorption process is strong enough to be detected in PACR.