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CuFeO₂ is a canonical magnetic-driven multiferroic with a triangular lattice network. It forms in the delafossite structure with space group R3-m at room temperature and undergoes a crystallographic phase transition to a monoclinic space group, C2/m, below the antiferromagnetic transition ~ 11 K. Using density functional theory (DFT), we examined the evolution of the coupling between the atomic and magnetic structure as a function of crystal symmetry. Phonon dispersion indicates a strong spin-lattice coupling which is driven mostly by differences in crystal symmetry of the high temperature and low temperature phases. Moreover, the phonon dynamics allowed us to determine that CuFeO₂ has long-range antiferromagnetic ordering. Our results for the calculated phonon dispersion are in good agreement with the experimentally observed phonon spectra.