Abstract: A semi-analytical method to investigate the free vibration characteristics of moderately thick functionally graded material(FGM)spherical torus structures with general boundary conditions was proposed. The theoretical formulas were derived by applying the first-order shear deformation theory, in which the displacement admissible functions were expressed by Improved Fourier Series to eliminate the discontinuity of the boundary. The general boundary conditions of the functionally graded spherical torus structure were simulated by different spring parameters. The natural frequencies of functionally graded spherical torus were obtained by Ritz method. The data in this paper were compared with those obtained by finite element method, experiment and literatures based on convergence analysis, and the influences of correlation parameter were studied. The results show that the proposed method has advantages of good convergence and high accuracy. The frequency parameter of functionally graded spherical torus structures increases with the increase of thickness and shear correction factors.