In this study, the out-of-plane response of sandwich curved beams with graphene platelet reinforced composite (GPLRC) face sheets and porous core under moving load is investigated. In the first step, the governing equations were derived based on the first-order shear deformation theory (FSDT) and using Hamilton’s principle. Then, in order to discretize the governing equations, the differential quadrature method (DQM) for the spatial domain and Newmark’s method in time domains were used. The effective elastic properties of face sheets were obtained using Halpin Tsai micromechanical model. At the interface of the core and face sheets, the same materials were considered to satisfy the material continuity. The other material properties were also obtained using the rule of mixtures. In the results section, firstly, the convergence and accuracy verification of the results were performed. Next, the effect of various parameters such as mass fraction, number of GPLRC layers used in the face sheets, distribution of graphene platelets in the core, opening angle of beam and speed of moving load on the natural frequency of system and dynamic response of the beam are analyzed. Numerical results showed that the existence of graphene platelets (GPLs) in the face sheets, the beam opening angle, and moving load on the natural frequencies and response of the beam was investigated. The results showed that the GPLs distribution pattern in the face sheets and core as well as the type of porosity affect the beam stiffness. It was also found that although increasing the number of GPLRC layers increases the beam stiffness, but the rate of increase of the natural frequencies gradually decreases by increasing the layer numbers.