This study investigates the free vibration characteristics of sandwich plates, which are composed of two isotropic faces and a porous core, using the analytical method based on the third order shear deformation theory. The core is reinforced uniformly by graphene nanoplatelet and composed of open or closed-cell foam with functionally graded pore distribution through the thickness direction. Four different porosity distributions are considered: a uniform and three functionally graded types. Comparison of the analytical results with the existing solutions in open literature and with those of finite element analysis (FEA) based on the shell element are made to verify the reliability of the presented analytical method. Characteristics of the open and closed-cell foams were investigated. Some numerical results are presented to check the influences of the weight fraction, geometry of the graphene nanoplatelet, porosity distribution, and porosity coefficient.