In this paper, hydroelastic behavior of a pontoon-type very large floating structure (VLFS) subjected to a moving single axle vehicle is computed using a novel numerical approach, in which the boundary element method (BEM) is firstly extended to cooperate with the moving element method (MEM), named the BEM–MEM. By utilizing this paradigm, the plate and fluid are discretized into "moving structural element" and "moving boundary element", respectively, which are conceptual elements and "travel" with the moving vehicle. Thus, the proposed method can absolutely eliminate the need of keeping track the location of the moving load with respect to the °oating structure. Particularly, the surrounding fluid is defined based on the potential flow theory and the motion of a floating plate is governed by the vibration equation of a thin plate. The governing equations of motion, moving element and fluid matrices of boundary element are formulated in a relative coordinate system traveling with the moving vehicle. Several examples are numerically conducted to illustrate the performance and ability of the BEM–MEM. Its obtained results are compared with those of the traditional finite element method for validation. The outcomes reveal that the proposed method is effective for the large-time behavior owing to the fact that it does not require a domain with the length greater than the horizontal displacement of the vehicle. The paper also discusses the effect of the liquid and structural parameters on responses of the vehicle and floating structure.