Free vibration analysis of a rectangular thick sandwich plate consisting of outer homogeneous layers with saturated nonhomogeneous Functionally Graded Porous (FGP) core has been conducted. Material property in this porous core could vary along the plate thickness according to Biot’s stress theory and other related functions. Solution to this problem was based on Quasi-Three-Dimensional shear deformation theory, which results the governing differential equations and the boundary conditions of the plate model. The boundary conditions in the considered plate model were clamped-simple-simple-clamped supports, whereas in the previous studies generally Navier method is used in which simple supports is assumed for all sides of the plate. In the present study, in order to obtain our proposed numerical solution, the differential quadrature method is applied. Among advantages of this method are being simple and straightforward, having reduced computational effort compared to other numerical methods and being capable of accounting for plates with different boundary conditions. Convergence and validation of the results with respect to the grid points were first presented. The effect of different core properties such as porosity, thickness, Skempton’s coefficient, total plate thickness, and different boundary conditions on FGP sandwich plate frequencies were investigated. Application of the latest theory for free vibration analysis of FGP sandwich plates is another main advantage of the presented method compared to other recent studies.