<p>Moving-load induced vibrations can, in certain instances, exceed those caused by equivalent static loads, especially at the critical velocity of moving loads. Suppressing these vibrations is of critical practical importance in various engineering fields, including the design of precision robotics and advanced aerospace structures where components are subject to moving loads. In this paper, an inertial nonlinear energy sink (NES) is used for the first time to reduce the vibration response of graphene platelet (GPL)-reinforced nanocomposite beams with elastic boundaries under moving loads. Based on the von Kármán nonlinear theory, the governing equations of the beam-NES system are derived using the Lagrange equation. The Newmark-Newton method, in conjunction with the Heaviside step function, is used to obtain the nonlinear responses of the beam under moving loads. The effects of the boundary spring stiffness, the GPL parameters, as well as the velocity and frequency of the moving loads on the beam response and the performance of the NES are thoroughly studied. The results of this work provide insights into applying NESs to suppress the nonlinear vibrations induced by moving loads in composite structures with elastic boundaries.</p>