The　nonlinear　vibrations　of　composite　laminated　plates　with　time-　dependent　base　excitation　and　boundary　conditions　are　investigated.　According　to　the　von　Karman　nonlinear　plate　theory,　the　dynamic　equations　of　motion　of　the　laminated　plates　are　established.　The　nonlinear　partial　differential　equations　are　transformed　to　the　nonlinear　ordinary　differential　ones　using　the　BubnovGalerkin＇s　method.　The　primary　resonance　and　the　primary　parametric　resonance　of　the　laminated　plate　with　timedependent　boundary　conditions　are　investigated　by　means　of　the　method　of　multiple　scales.　The　validity　of　the　present　theoretical　method　is　verified　by　comparing　the　amplitudefrequency　relationship　curves　acquired　from　the　present　theoretical　method　with　those　calculated　from　the　numerical　simulation.　The　amplitude-　frequency　characteristic　curves　and　the　displacement　time　histories　for　different　ply　angles　of　the　composite　laminated　plate　are　analyzed.　The　effects　of　the　viscous　damping　factor　and　the　transverse　displacement　excitation　on　the　amplitude-　frequency　relationship　curves　are　also　studied.　The　present　results　are　helpful　for　the　nonlinear　dynamical　analysis　and　design　of　the　composite　laminated　plate　with　time-　dependent　boundary　conditions.