Viscoelasticity is a property of materials that exhibit both viscous and elastic characteristics. In linear viscoelasticity, the stress is linearly related to the history function of strain. This paper discusses vibration analysis of functionally graded viscoelastic rectangular plate. The viscoelastic behavior of the plate is modeled using the Zener three-parameter model. Also, the material properties of the plate are graded through the thickness according to the volume fraction model. The maximum stress and strain are calculated based on the linear first-order shear deformation theory and the simply support boundary conditions is assumed at all four edges of the plate. A code is prepared using the Mathematica software to obtain the frequency values and effect of inherent and geometric characteristics of the sheet on natural frequency of the plate. These effects are studied using the tables and graphs represented in the results and discussion section of the paper. The results obtained in this paper are simplified to a functionally elastic plate to compare with those given in the literature search. The comparison of results shows good agreement against data given in literature for both cases.