An analysis on the nonlinear vibrations of a simply-supported composite laminated rectangular plate with parametrical excitations and forcing excitations is presented. First, based on the Reddy’s high-order shear deformation theory and the model of the von Karman type geometric nonlinearity, nonlinear governing partial differential equations of motion are derived by using the Hamilton’s principle. The plate has linear external damping. Then, used the second-order Galerkin discretization approach, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations under parametrical excitations and forcing excitations, which deals with the periodic and chaotic oscillations. The method of multiple scales can be used to get four averaged equations. From the averaged equations obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, high-dimensional Melnikov method is utilized to analyze the global bifurcations and chaotic dynamics in composite laminated rectangular thin plates. The results obtained above mean the existence of the chaos for the Smale horseshoe sense in parametrically excited and forcing excited composite laminated plates. The chaotic motions of composite laminated plates are also found by using numerical simulation. Numerical simulations obtained in this paper indicate that there exist different shape of the chaotic responses in the nonlinear oscillations of the composite laminated plate under certain force excitations, parametric excitations, parameters and initial conditions.