In　this　paper,　the　nonlinear　oscillations　and　chaotic　dynamics　of　a,　parametrically　excited　simply　supported　symmetric　cross-ply　laminated　composite　rectangular　thin　plate　are　further　investigated.　Considering　geometric　nonlinearity　and　nonlinear　damping,　a　two-degree-of-freedom　nonlinear　system　under　parametric　excitation　is　obtained　to　give　the　nonlinear　governing　equations　of　motion　for　laminated　composite　plate　subjected　to　in-plane　load.　The　method　of　multiple　scales　is　utilized　to　obtain　the　averaged　equations　that　are　numerically　solved　to　obtain　the　steady　bifurcation　responses　and　analysis　of　stability　for　laminated　composite　thin　plate.　It　is　illustrated　that　under　certain　conditions　laminated　composite　thin　plate　may　have　the　multiple　steady　bifurcation　solutions　and　jumping　may　occur.　The　chaotic　motion　of　rectangular　symmetric　cross-ply　laminated　composite　thin　plate　is　also　found　by　using　numerical　simulation.　It　is　found　that　the　occurrence　of　the　periodic,　quasi-periodic　and　chaotic　motions　for　a　parametrically-excited　four-edges　simply　supported　rectangular　symmetric　cross-ply　laminated　composite　thin　plate　depends　on　the　parametric　excitation.