In this paper, non-linear dynamics analysis of functionally graded material (FGM) shell structures is investigated using the higher order solid-shell element based on the Enhanced Assumed Strain (EAS). With this element, a quadratic distribution of the shear stress through the thickness is considered in an enhancing part. Material properties of the shell structure are varied continuously in the thickness direction according to the general four-parameter power-law distribution in terms of the volume fractions of the constituents. Performance and accuracy of the present higher order solid-shell element are confirmed by comparing the numerical results obtained from finite element analyses with results from the literature.