A new type of lithium niobate beam with an inversion layer was investigated in this study. The symbols for the piezoelectric constants of this inversion layer were the opposite of those of a regular layer. Thus, the bending vibration of the lithium niobate beam could be excited by an electric field in the thickness direction. The displacement and potential were expressed in a power series form along the thickness and width directions of the beam, and one-dimensional equations of the bending motion of the lithium niobate beam were derived. These one-dimensional equations were used to analyze the dispersion relationship of the wave propagating along the length direction of the beam in order to verify its accuracy. The dispersion curves obtained from these one-dimensional equations coincided with those obtained using the three-dimensional theory in a small wavenumber range. The output power density and output efficiency of a beam-type piezoelectric energy harvester were analyzed using the one-dimensional equations. The results were compared with those derived using the two-dimensional and three-dimensional theories. The results indicated that the results obtained from the one-dimensional equations were very close to those obtained using the three-dimensional equations, suggesting their great application potential in the field of piezoelectric devices.