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In this study, vibration response of functionally graded plate resting on a viscoelastic foundation is studied. An analytical solution is proposed using a high-order shear deformation theory with only four unknowns, which means that the current theory has few unknowns compared to the first and other high shear deformation theories. The present theory uses a displacement field with integer terms instead of derivative terms by also including the shear deformation effect without introducing the shear correction factors. The mathematical model of the foundation used followed the Winkler–Pasternak two-coefficient model, with an additional term added to represent the damping effect. The governing equations were generated using the principle of virtual works. Subsequently, the analytical solution is based on Navier's principle to solve the vibration problem of a simply supported FG plate resting on a viscoelastic foundation. Some numerical results are presented to demonstrate the impact of the material index, the type of elastic foundation and the damping coefficient of the foundation on the dynamic response of FG plates resting on viscoelastic foundations. In the end, it is concluded that the current results with the proposed theory are found to be in good agreement with the other available results and this theory can easily be used to solve the free vibration problems of FGM plates resting on visco-Pasternak medium. [ABSTRACT FROM AUTHOR]