Abstract: The discontinuous phenomenon of stress and electric displacement caused by the material differences between layers appears when the conventional Laguerre polynomial approach is used to solve the problem of layered half-space structures. To overcome this shortcoming, an improved Laguerre polynomial approach is proposed to investigate the propagation characteristics of Love waves in functionally graded piezoelectric layered half-spaces. By comparison with the results of WKB method published in the literature, the validity of the improved approach is verified. The corresponding dispersion curves, stress and electric displacement profiles are calculated and analyzed. The results show that the improved approach can avoid the above-mentioned discontinuous phenomenon. The stress and electric displacement of the high frequency Love waves mainly distribute on the side of low velocity material in the functionally graded piezoelectric layer. The study in this paper lays a theoretical basis for the design and optimization of Love wave sensors.