In the study of the aero-engine compressor blades, the blade is simplified as a rotating cantilever FGM plate with varying rotating speed. Based on the Reddy's high-order shear deformation theory and the von Karman type equations for the geometric nonlinearity, the nonlinear governing partial differential equations of motion are derived by using the Hamilton's principle. The aerodynamic load is determined by using the first-order piston theory. The Galerkin approach is used to transform the nonlinear partial differential governing equations of motion into a two-degree-of-freedom nonlinear system. The principal parametric resonance and the 1:1 internal resonance are considered. The asymptotic perturbation method is used to obtain a four-dimensional nonlinear averaged equation. The numerical method is used to find the nonlinear dynamic responses of the rotating cantilever FGM plate. It is found the rotating speed has an important influence on its nonlinear dynamic behavior. It is shown that, at different rotating speeds, there exist the chaotic, periodic and quasi-periodic motions for the rotating cantilever FGM plate.