When the rate 1/tau of electron scattering by impurities and/or phonons is comparable to the frequency omega of an electromagnetic radiation, the electron transitions among different states are accompanied by absorption of radiation. Far-infrared resonant absorption of radiation in a quantum wire (QW) at strong magnetic fields B is studied. The radiation is taken polarised along the QW (x axis) and B is applied normal to it (a axis). The confining potential along the y and z axes is assumed parabolic and triangular, respectively. The results show that: 1) similar to the case of a two-dimensional electron gas (2DEG), resonant absorption occurs in a QW when the electron temperature T-e is in the range from 80 K to 150 K; 2) one absorption peak can be observed at f = omega/2 pi similar to 0.1 THz for T-e similar to 80 K, whereas for a 2DEG, at the same T-e, it occurs at f = omega/2 pi similar to 0.5 THz; 3) With increasing T-e the peak shifts to higher frequencies and broadens markedly; 4) with increasing B, the peak shifts to higher frequencies and the absorption intensity first increases and then decreases; 5) the application of B does not result in a significant broadening of the absorption peak. As a result, applying a strong B-field to a QW provides a means of controlling the rate 1/tau and leads to a frequency-tunable resonant absorption.