Sandwich plates play an important role in advanced industries such as aerospace, transportation, and modern structures due to their high stiffness-to-weight ratio. The use of anisogrid lattice cores with functionally graded graphene platelet-reinforced nanocomposite face sheets is a novel approach to improve the vibration characteristics and dynamic performance of these structures. On the other hand, the analysis of the response of these plates under moving load is of particular importance due to the dynamic nature of the loading. The main objective of this research is to analyze the free vibration and dynamic response of sandwich plates with anisogrid lattice core and functionally graded graphene platelet-reinforced nanocomposite face sheets under moving load and to investigate the effect of geometric, mechanical, and reinforcement parameters on the dynamic behavior of the structure. In this regard, the high-order shear deformation theory has been used to model the mechanical behavior of the plate. The effective properties of the face sheets were determined using the modified Halpin-Tsai micromechanical model and the core of the anisogrid lattice was modeled as an equivalent continuous homogeneous environment. The governing equations were discretized using the finite element method in the spatial domain and the dynamic response of the system under moving load was calculated using the Newmark time integration method. The model was validated by convergence analysis and comparison of natural frequencies with results from other scientific sources. The results showed that the distribution pattern of graphene platelets, the weight fraction of graphene platelets, the geometric characteristics of the anisogrid lattice core, the boundary conditions and the moving load velocity have a significant effect on the natural frequencies and dynamic displacement amplitude of the plate. It was observed that the plate with face sheets with the FG-V distribution pattern had the lowest