Recently, bonded structures comprising a quartz substrate and a LiNbO3 (LN) or LiTaO3 thin-plate have been attracting attention as a means of obtaining enhanced properties for surface acoustic wave (SAW) devices. It was reported that the bonding strength was extremely improved by utilizing an amorphous thin film as a middle layer. In this research, the propagation and resonance characteristics of longitudinal leaky SAWs on an amorphous layer inserted to the boundary between an X-cut 36°Y-propagating LN (X36°Y-LN) and X35°Y-quartz were investigated. For the metallized surface of an X36°Y-LN/Al2O3/X35°Y-quartz structure, an attenuation of 0.0001 dB /λ was obtained at an LT thin-plate thickness of 0.072λ (λ: wavelength), which was better than that of an X36°Y-LN/X35°Y-quartz structure. Utilizing a finite element method, we found that the admittance ratio and Q factor for the X36°Y-LN/Al2O3/X35°Y-quartz model were improved owing to the reduction of the leakage due to the shear-vertical particle displacement.