The nonlinear dynamic response of functionally graded (FGM) rectangular plates under combined transverse and in-plane excitations are investigated under the different internal resonance. The material properties are assumed to be temperature-dependent and vary along the thickness direction. The thermal effect due to one-dimensional temperature gradient is included in the analysis. The governing equations of motion for FGM rectangular plates are derived by using Reddy’s third-order plate theory and Hamilton’s principle. The Galerkin’s approach is utilized to reduce the governing differential equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms, which are then solved numerically by using 4-th order Runge-Kutta algorithm. The resonant case considered herein are 1:1, 1:2 and 1:3 internal resonance and principal parametric resonance-1/2 subharmonic resonance. The effects of plate geometry parameters, in-plane excitations and temperature field on the internal resonance relationship and nonlinear dynamic response of FGM plates are studied. Numerical results show that in the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance, the vibration amplitude of the plate center is much greater than the other two cases of the internal resonance.