Composite laminated plates have many advantages such as unique electromechanical coupling, light weight, high strength, fatigue resistance, and it is widely used in modern engineering and especially in the aerospace industry. In the present study, based on the third-order shear deformation laminate theory of Reddy, we study the six-dimensional nonlinear system for the simply supported at the four-edge rectangular laminated composite piezoelectric rectangular plates, which are subjected to in-plane excitations, out-plane loads, thermal loads and piezoelectric excitations. Taking into account that the averaged equation has a double zero and two pairs of pure imaginary eigenvalues, we use the theory of normal form to simplify the six-dimensional averaged equation to a simpler form. The energy-phase method is employed to study the global bifurcations and chaotic dynamics of the six-dimensional nonlinear system for a composite laminated plate. The global analysis indicates that there exists the multi-pulse jumping of homoclinic orbits in the system. At the same time, numerical simulation is used to investigate the nonlinear characteristic of the plate. The results of numerical simulation demonstrate that the jumping phenomena of orbits can occur for the composite laminated plate.