Far-infrared reflectivity measurements of Cs₂CdBr₄ crystal were performed over the frequency region 15-600 cm^-1 and temperature region 10-297 K. All transverse lattice modes have frequencies below 230 cm^-1 because of the heavy atoms in the Cs₂CdBr₄ crystal. A sequence of phase transitions can be identified on the basis of the activation of new modes below the phase transition temperatures due to the lowering of the crystal symmetry on cooling. Factor-group analysis was carried out and selection rules found for the infrared activity of phonon modes in the incommensurate and commensurate phases, and the results were compared with the experimental data.