In this paper, a formulation for calculating the effective permittivity of a piezoelectric layered SAW structure is given, and the exact frequency response of ZnO/diamond/Si-layered SAW is calculated. The effective permittivity and phase velocity dispersion of a ZnO/diamond/Si-layered half space are calculated and discussed. The frequency response of an unapodized SAW transducer is calculated, and the center frequency shift caused by the velocity dispersion is explained. In addition, the electromechanical coupling coefficients of the ZnO/diamond/Si -layered half space based on two different formulas are calculated and discussed. Finally, based on the results of the study, we propose an exact analysis for modeling the layered SAW device. The advantage of using the effective permittivity method is that, not only the null frequency bandwidth, but also the center frequency shift and insertion loss can be evaluated.