Far-infrared reflection spectra in the wavenumber region between 15 to 500 cm-1 are obtained and studied for the mixed crystals CdxHg1-xTe with different compositions from 0.18 to 0.45 at the temperatures between 4.2 to 300 K. In addition to the fine structures of the CdTe-like optical phonon reflection band, the complex structure of the HgTe-like band for the low composition sample has been observed, and the dependences of the spectral structures on the composition and the temperature of the samples have also been investigated. The fine structures of the reflection spectra are explained based on the multimode quasi-harmonic oscillator model.By means of the classical oscillator matching method, the curve-fitting calculations are performed for the experimental reflection spectra, and the dielectric function spectra and other optical constants versus frequencies are obtained from a satisfactory fitting.