In this study, the nonlinear dynamic response of a hybrid laminated composite plate composed of basalt, Kevlar/epoxy and E-glass/epoxy under the blast load with damping effects has been investigated. The von Kármán type of geometric nonlinearities are taken into account and the rectangular composite plate is assumed to be simply supported on all edges. The Galerkin Method is used to obtain the nonlinear differential equations in the time domain, and those equations are solved by Finite Difference Method. Parametric studies are conducted. The influences of some parameters such as damping ratios, aspect ratios and different peak pressure values have been investigated.