For the nonlinear equations of thickness-shear vibration and flexural vibration of quartz crystal plate considering geometric and material nonlinearity, the equations are transformed and solved by the newly proposed extended Galerkin method. The strongly coupled frequency-response relationships of thickness-shear and flexural vibrations of quartz crystal plate are obtained respectively, and the frequency-response curves under the influence of different amplitude ratios and different driving voltages are drawn. The numerical results show that the optimal aspect ratio size of quartz wafer should be selected to avoid the strong coupling of the two modes. The change of driving voltage will cause the obvious change of thickness-shear vibration frequency of quartz crystal resonator. The frequency shift value must be controlled within the allowable value of common piezoelectric acoustic devices. The solution of high frequency nonlinear vibration equations of quartz crystal plate by extended Galerkin method lays a foundation for nonlinear finite element analysis and partial field effect analysis.