In this paper, free vibration of functionally graded annular plates on elastic foundations, based on the three-dimensional theory of elasticity, using state-space based differential quadrature method for different boundary conditions is investigated. The foundation is described by the Pasternak or two-parameter model. Assuming the material properties having an exponent-law variation along the thickness, a semi-analytical approach that makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is used to obtain the vibration frequencies. Supposed state variables in the present method are different from what have been used for functionally graded annular plate so far. They are a combination of three displacement parameters and three stresses parameters. Numerical results are given to demonstrate the convergency and accuracy of the present method. In addition, the influences of the Winkler and shearing layer elastic coefficients of the foundations and some parameters are also investigated.