Moving　loads　induced　nonlinear　vibrations　in　beams　are　commonly　encountered　in　various　engineering　applications,　and　the　resulting　responses　can　be　greater　than　those　under　equivalent　static　loads.　In　this　paper,　an　inertial　nonlinear　energy　sink　(NES)　is　used　for　the　first　time　to　reduce　the　nonlinear　vibration　of　graphene　platelet　(GPL)　reinforced　porous　nanocomposite　beams　under　moving　loads.　Based　on　the　von　K　&　aacute;rm　&　aacute;n　nonlinear　theory,　the　governing　equations　of　the　GPL　reinforced　metal　foam　beam　with　an　inertial　NES　are　derived　using　the　energy　method　and　Lagrange　equation.　The　Newmark-Newton　method　combined　with　the　Heaviside　step　function　is　adopted　to　determine　the　nonlinear　responses　of　the　beam　under　moving　loads　of　constant　amplitude　and　harmonic　excitation.　An　optimization　procedure　is　conducted　to　optimize　the　NES　parameters　to　enhance　the　effectiveness　of　the　inertial　NES　under　different　moving　load　conditions.　The　optimized　inertial　NES　can　effectively　reduce　the　maximum　deflection　of　the　beam　and　achieve　better　overall　performance.　The　results　of　this　paper　provide　an　important　reference　for　understanding　and　applying　inertial　NES　to　suppress　the　vibration　of　composite　structures　induced　by　moving　loads.