In the present paper, the modified screening interaction potential was adopted to investigate the dust lattice waves in dusty ring. Firstly, the influence of parameter ε on the modified screening interaction potential was analyzed; and it was found that the parameter ε has a long-range effect on the pairwise interaction between the particles. Secondly, the dispersion relations of longitudinal and transverse waves are obtained, and the effect of long-range action parameter ε, dimensionless lattice parameter α and dimensionless shielding parameter on the dust lattice waves propagation in dusty ring are studied. Some interesting phenomena, such as the coupling of longitudinal and transverse waves, and instabilities of transverse waves are found, which are in good agreement with some previous works. Finally, the transverse wave instabilities and the relevant critical lattice parameter αc are presented and discussed.