Based on lattice dynamics,considering the central in-plane elastic forces of the interatomic interaction,the dispersion relations of two-dimensional equilateral hexagonal lattice were derived,and the expressions of the dispersion relations along Γ-M,M-K and Γ-K three symmetry directions were obtained in the first Brillouin zone. There are four pieces of lattice waves in each direction,where two branches are acoustic waves and other two are optical waves. The effects of the nearest neighbor and secondary neighbor coupling to the dispersion relations were discussed. The results show that,in only nearest neighbor coupling,the eigen frequencies of two acoustic modes are zero and other two non-zero values which correspond to optical modes are degenerate at Γ point. One high frequency acoustic branch and one low frequency optical branch are degenerate at K point,and all four branches are nondegenerate at M point. One of the acoustic branches has totally zero frequencies and one optical branch is dispersionless over the entire symmetry directions. There is a frequency gap between acoustic branches and optical branches along Γ-M direction,and no frequency gap in other directions. With enhancement of the secondary neighbor coupling,the phonon frequencies are increased,and all four branches are displayed distinct dispersion along three directions,and the frequency gap is narrowed along Γ-M direction. The above results indicate that the dispersion relations are remarkably affected by the secondary neighbor coupling. But it has no influence on the value and degeneracy of the phonon frequency at Γ point,and it also has no effect on the degencracy of the phonon frequency at k point.