Abstract: The dispersion of Love waves is studied in afunctionally graded elastic half-space covered with a functionally gradedmaterials layer and the general form of Love wave dispersion equation isobtained. In the functionally graded elastic half-space and thefunctionally graded covered layer, the motion control equations for the antiplaneshear wave are solved, the analytical solutions for displacement and stressare obtained, and with these analytical solutions, the dispersion equation of Lovewave is obtained. As an example, with the properties of the coveredlayer, theshear elastic modulus and mass density, varing gradually in exponentialforms, and those of the half-space varing gradually in parabolicforms, the dispersion equations are solved by using the iteration method and thecurves of dispersion are obtained. The results show that cut-off frequencyappears in the dispersion curve of the lowest mode.