In this paper, the non-linear (NL) behavior of composite truncated conical shells subjected to dynamic loading is studied. The basic equations are derived using the von Karman-Donnell-type of kinematic nonlinearity. These equations are reduced to a NL differential equation with the variable coefficient using the superposition principle and Galerkin method. The resulting equation is solved numerically using Runge-Kutta method and modified Budiansky-Roth criterion and the values of dimensionless NL critical time parameters are obtained. Finally, the effects of axial loading speed and orthotropy on the dimensionless NL critical time parameters of composite truncated conical shells are investigated.