Abstract: The dispersion problem of Love wave in the homogeneous elastic half-plane covered with a functionally graded materials layer is studied, and the general form of Love wave dispersion equation is presented. By using of the WKBJ approximation method, the closed-analytical solutions of displacement and stress in functionally graded materials layer are obtained, and the general form of Love wave dispersion equation is educed. The properties of functionally graded materials whose shear modulus and mass density are gradually varing in exponential forms along the thickness are calculated and analyzed. The curves of dispersion are presented and the general properties of Love wave propagation in the elastic half-plane covered with a functionally graded materials layer are discussed. This can provide basis for nondestructive tests or the inversion analysis of wave motions.