In this study, the geometrically nonlinear dynamic behaviour of simply supported tapered laminated composite plates subjected to the air blast loading is investigated numerically. In-plane stiffness, inertia and the geometric nonlinearity effects are considered in the formulation of the problem. The equations of motion for the tapered laminated plate are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. Then, the Galerkin method is used to obtain the nonlinear algebraic differential equations in the time domain. The resulting equations are solved by using the finite difference approximation over the time. The effects of the taper ratio, the stacking sequence and the fiber orientation angle on the dynamic response are investigated. The displacement-time and strain-time histories are obtained on certain points in the tapered direction. The results obtained by using the present method are compared with the ones obtained by using a commercial finite element software ANSYS. The results are found to be in an agreement. The method presented here is able to determine the nonlinear dynamic response of simply supported tapered laminated plates to the air blast loading accurately.