In　this　paper,　nonlinear　dynamics　of　a　simply　supported　antisymmetric　cross-ply　laminated　composite　thin　rectangular　plate　under　parametric　excitation　is　investigated.　The　governing　equations　of　motion　for　the　antisymmetric　cross-ply　laminated　composite　plate　are　derived　by　using　von　Karman　type　plate　equation.　The　geometric　nonlinearity　and　nonlinear　damping　are　included　in　the　governing　equations　of　motion.　A　two-degree-of-freedom　parametrically　excited　nonlinear　system　including　the　quadratic　and　cubic　nonlinear　terms　is　obtained　by　using　the　Galerkin　method.　Based　on　the　Fourier　expansion　and　the　temporal　rescaling,　an　asymptotic　perturbation　method　is　utilized　to　obtained　four-dimensional　nonlinear　averaged　equations　on　the　amplitude　and　the　phase　of　nonlinear　oscillations　of　the　antisymmetric　cross-ply　laminated　composite　plate　for　the　first　time.　Based　on　the　averaged　equations,　the　steady　state　nonlinear　responses　and　their　stabilities　are　determined　by　using　numerical　approach.　The　relations　between　the　steady　state　nonlinear　responses　and　the　amplitude　and　frequency　of　parametric　excitation　are　obtained.　Under　the　certain　conditions,　the　antisymmetric　cross-ply　laminated　composite　plate　may　have　two　steady　state　nonzero　solutions　in　which　the　jumping　phenomenon　occurs.