Hg1-xZnxTe crystals were grown by the traveling heater method. The composition and crystalline quality of ingots were analyzed by electrolyte electroreflectance experiment. The far-infrared reflection spectra of Hg1-xZnxTe crystals with various composition x were measured at temperatures ranging from 90 K to 295 K in the wavenumber region of 60 to 450 cm(-1). In all but the pure compounds, HgTe and ZnTe, a two TO phonon structure was clearly observed. The optical phonon frequencies were well-determined by both the Kramers-Kronig integrations and the dynamic dielectric function fitting, and their temperature dependence is discussed.