This paper presents a two-variable refined plate theory for free vibration of functionally graded material (FGM) plates lying on viscoelastic Winkler–Pasternak foundations. The present work aims to examine the vibrations by a higher-order shear deformation theory including a new function of warping. The governing equations are derived from the principle of virtual displacements. Some illustrative examples are given in an attempt to solve the free vibration problem of a rectangular plate with various boundary conditions. The effects of damping on free vibrations, considering various parameters, are examined in detail. In the end, it is concluded that the present results with the new shear shape function of viscoelastic foundation are found to be in good agreement with other available results and the proposed method can easily be used to solve free vibration problems of the FGM plates.