Abstract: As a new type of material, functionally graded material (FGM) has attract wide attention and application in recent years due to its good mechanical properties. For the metal-ceramic FGM circular plate with clamped boundary condition, the mode function in polynomial form and the Galerkin method are adopted to derive the longitudinal and transverse coupling nonlinear vibration equations of the system under rotational motion and thermal effects, and the static deflection caused by rotation and density difference is also obtained. The improved multi-scale method is used to solve the equations, and then the frequency-amplitude response equation and analytical solution of the strong nonlinear system are obtained. Based on calculation examples, the amplitude-frequency curves, amplitude-excitation force curves, and amplitude-temperature curves of the FGM plate are presented, and the influence of different physical parameters on the resonance amplitude of the structure is analyzed. Reasonable consistence is evident by comparing the analytical and numerical solutions.