This paper presents the dynamic analyses of composite sandwich plate resting on a Winkler viscoelastic foundation under moving load using the Multi-layer Moving Plate Method (MMPM). The governing equations of motion of composite sandwich plate are established in a moving coordinate system attached to the moving load. The main convenience is that the load is static in this coordinate system, which avoids the updating of load locations due to the change of the contact points with the elements. To verify the accuracy of the MMPM, the dynamic analyses of composite sandwich plate are investigated. Next, the effects of load velocity on the dynamic responses of composite sandwich plates are examined.