The cyclotron resonance of the conduction electrons in N-Hg1-xCdxTe was observed and the high-resolution CR line-shapes traces for a series of far infrared laser radiation with different wavelengths were obtained by using a FIR Laser Magnetospectrometer. The theoretical calculation shows that the characterization of the CR line-shapes and its dependence on some physical parameters can be well described by the classical Drude theory. In addition, the relaxation time is determined by fitting the theoretical result to the experimental lin-shape and compared to that obtained from the electron mobility.The theoretical aspect of the difference between them is discussed.