An effective method， namely spectro geometric method-pseudo excitation method （SGM-PEM）， is presented to investigate the stationary random vibration characteristic of functionally graded annular plates with complex boundary conditions. The boundary constraint springs are uniformly arranged along each boundary edge of the annular plate to stimulate the complex boundary conditions. The stationary random excitation is transformed into the pseudo harmonic excitation by using the pseudo excitation method （PEM）. The displacement admissible functions of the annular plate are described based on the spectrgeometric method which only contains concise trigonometric function within the framework of the first-order shear deformation theory. The dynamic analysis model of functionally graded annular plate under stationary random excitation is established with the Rayleigh-Ritz method.Compared with the results obtained with finite element method （FEM）， the effective and accuracy of the proposed method are demonstrated. The influence laws of some factors which include gradient index， thickness， and boundary conditions on the stationary random vibration characteristics of functionally graded annular plates are analyzed.