Lamb waves propagating in piezoelectric plate covered by thin-film electrodes with arbitrary conductivity are investigated. The structure consists of three parts, piezoelectric plate, top and bottom thin films with arbitrary conductivities, and top and bottom free space. The governing equations in each part are first solved, and then, continuous conditions are used to form the propagating matrix. Finally, the dispersion equations are obtained by boundary conditions. Calculating the dispersion equations with different conductivities, the dispersion curves in high conductivity and zero conductivity are compared. The wave mode shapes of different branches are investigated, including the distributions of mechanical displacements and stresses in the piezoelectric plate and distributions of electrical displacement and potential in both plate and free space. The relationships between frequency difference and wave mode shapes in zero and high conductivity are investigated. Furthermore, the dispersion curves of general conductivity are calculated. The attenuation of waves is compared in different branches and different conductivities. The wave mode shapes are also calculated and compared with the cases in zero and high conductivities.