To obtain bonded structure with a low residual stress and a low attenuation for longitudinal leaky surface acoustic waves (LLSAWs), the propagation and resonance properties of an LLSAW on an amorphous layer inserted between LiNbO3 (LN) thin plate and an X-cut quartz substrate were theoretically analyzed. The attenuation of LLSAW on the metallized surface of an X-cut 36°Y-propagating LN (X36°Y-LN)/Al2O3/X35°Y-quartz structure was calculated to be 0.0001 dB/λ at the normalized LN thin-plate thickness h/λ=0.072 (λ: wavelength) and was lower than that on an X36°Y-LN/X35°Y-quartz structure. Using a finite element method (FEM) system for analysis, for the X36°Y-LN/Al2O3/X35°Y-quartz model, we found that the Q factor was improved to 82,000 from 15,000 for the X36°Y-LN/X35°Y-Q model. It is considered that the attenuation was reduced by the suppression of the leakage of the shear vertical component when the Al2O3 layer was inserted. For the same structure, but in which the mechanical loss Qm of 1,000 for LN was assumed, the Q factor was determined to be 2,500 and 1,900 with and without an inserted amorphous Al2O3 layer, respectively.