The propagation characteristics of the leaky surface acoustic wave (LSAW) propagating on rotated Y-X lithium niobate (LiNbO3) substrates with a ferroelectric inversion layer are theoretically analyzed. The results show that the attenuation of the LSAW on 41° Y-X LiNbO3 is smaller than 10-5 dB/wavelength over a range of kh (k: wave number, h: inversion-layer thickness) from 2 to 2.5 for both free- and metallized-surface cases, and that the phase velocity of the LSAW is decreased and the concentration of the displacement to the surface is improved by the electric-field short-circuiting effect of the domain boundary. The propagation characteristics of the surface acoustic wave on 128° Y-X LiNbO3 substrates with an inversion layer are also reported.