The relation between the phonon frequency of vibration of crystal and the propagation of the wave vector (q) is known as the dispersion relation. A graph between the phonon frequency and wave vector (q) is called the dispersion curve. A calculation of the phonon dispersion curve was carried out using a lattice model for inter-atomic forces and the results of the calculation were compared with experimental data. The theoretical prediction was found to be in agreement with the experimental data. The three-body forces of lattice dynamics of face-centered cubic (FCC) metals was found to play an important role, whereby the involvement of such three-body forces improved the agreement between the experimental and the theoretical phonon dispersion curves. The developed procedure of the calculation of phonon frequencies of FCC metals has relevance in understanding the theory of lattice vibration, the structure of FCC metals, and the reciprocal lattice of FCC metal’s structure. The method involves the derivation of the formula to be used to obtain the values of the phonon frequencies of FCC metals. The developed calculation was used in the computation of phonon frequencies corresponding to various values of reduced wave vector in the Brillouin zone along [100], [110], and [111], and the symmetry direction which corresponds to the various values in the Brillouin zone and along the direction for copper (Cu), silver (Ag), gold (Au), and cobalt (Co). The dispersion curve was in very good agreement with the experiment values or results.