In this study, propagation characteristics of surface acoustic waves in a layered piezoelectric structure (AIN/128°Y-X LiNbO3) and/or thin metal films deposited at various interfaces are calculated numerically. The effects of the polarity of 128°Y-X LiNbO3 on SAW characteristics are illustrated. The calculated phase velocity and coupling coefficient of SAWs in the IDT/ZnO/128°Y-X LiNbO3 structure are also demonstrated for comparison. The simulation results obtained in this study can be applied to the design of SAW devices using AIN/128°Y-X LiNbO3 structures.