The static equilibrium equation of a functionally graded circular plate was established by using elastic theory, and the neutral plane site of the functionally graded circular plate was determined. On this basis, the nonlinear vibration and buckling differential equations for the functionally graded circular plate in uniform temperature field were derived,the approximate solution to nonlinear thermal vibration and buckling of the functionally graded circular plate was obtained, the effects of neutral plane site, gradient index and temperature on nonlinear thermal vibration and buckling of the functionally graded circular plate were discussed and analyzed. The comparison of the calculation results by this method with these by finite element method verified the method was correct. Analysis on examples indicates that the neutral plane site has certain influence on nonlinear thermal vibration and buckling of the functionally graded circular plate in uniform temperature field.