The propagation of Love wave in a phononic crystal consisting of superlattice lithium niobate substrate carrying a piezoelectric waveguide layer is analyzed. The interface between the waveguide layer and the substrate is imperfectly bonded, which is described by means of a shear spring model. Numerical results show that the bandgap shifts to a lower frequency range and the bandwidth decreases as the interface imperfection increases. Moreover, the transmission coefficient calculations using finite element simulation revealed that a perfect interface results in more effective bandgap attenuation.