Responses of floating plates with the impact of moving excitations have been previously studied by several scholars. Generally, such structures were often assumed to be isotropic. Nonetheless, the directional-dependent bending stiffness should be considered for designing practical floating structures, especially for ver y large floating structures. Accordingly, this article aims to analyze hydroelastic responses of floating composite plates subjected to moving loads for the first time. For this, a novel numerical approach as a combination of boundar y element method and moving element method which is named the BEM–MEM is proposed. In the this approach, governing equations of motion, moving element, and fluid matrices are formulated in a relative coordinate system traveling with moving loads. Consequently, the suggested paradigm can effectively eliminate difficulties in addressing the bound of computational domain and tracking the location of contact points which often encounter in the traditional finite element method owing to utilizing a fixed coordinate system. Several numerical examples are exhibited to demonstrate the performance and ability of the boundar y element methodmoving element method . Gained results are compared with those by the Fourier transform method and the asymptotic expression to verify the accuracy of the proposed methodology. The outcomes indicate that the speed of moving loads considerably affects the plate deflection. In addition, as the speed is larger than the minimum celerity of the free surface of hydroelastic system (Cmin), the influence of anisotropy on the deflection becomes significant.