In　this　article,　the　natural　vibration　investigation　of　a　functionally　graded　material　sandwich　plate　with　initial　geometrical　imperfection　of　the　exponential　function　is　conducted.　Two　face　sheets　of　the　sandwich　plate　are　composited　by　functionally　graded　material.　Their　material　coefficients　are　affected　by　temperature　and　vary　in　the　direction　of　thickness　following　the　power　law.　The　core　layer　is　only　the　metal.　With　the　aid　of　Reddy＇s　displacement　fields,　a　quasi-three-dimensional　model　is　used,　in　which　the　effects　of　transverse　stretching　on　natural　vibration　are　considered.　The　natural　frequencies　and　model　shapes　of　the　system　are　calculated　on　the　basis　of　Rayleigh-Ritz　method　and　Chebyshev　polynomials.　A　comparison　of　these　results　with　those　of　the　existing　three-dimensional　theory　results　shows　the　validity　and　computability　of　present　method.　The　influences　of　various　parameters　on　the　natural　frequencies　are　researched　in　detail.