The wing is simplified as the cantilever plate model based on the engineering background of the aircraft wing. The nonlinear dimensionless partial differential governing equations of the composite cantilever piezoelectric plate under the combination of transverse and in-plane excitations are established by using the Hamilton′s principle. Galerkin approach is used to discretize the partial differential equations to the ordinary differential equations with two-degree-of-freedom under the transverse and parametric excitations. Meanwhile, the method of multiple scales is employed to obtain the fourdimensional averaged equation considering the primary parametric resonance1∶3 internal resonance. Numerical method is utilized to find the nonlinear dynamics responses of the composite piezoelectric cantilever plate. The numerical results indicate the existence of the periodic and chaotic responses. The influences of the transverse excitation and piezoelectric parameter term on the bifurcations and chaotic behaviors of the composite piezoelectric cantilever plate are investigated. The conclusions are instructive to the practical engineering.