In this work, nonlocal dynamic formulation of a graphene nanoplatelets reinforced composite doubly curved micro/nano shell is presented based on Hamilton's principle using a shear deformable model. The structure is composed of a honeycomb core integrated with graphene nanoplatelets reinforced face-sheets. The material properties of honeycomb core are computed using available formula in literature. Furthermore, material properties of composite reinforced face- sheets are assumed to vary along the thickness direction based on Halpin-Tsai micromechanical models and rule of mixture. The size-dependent governing equations of motion are derived through employing nonlocal equations. After verification of the formulation and solution procedure using a comparative study, the large parametric results are presented to discuss impact of main geometric, material and small scale parameters on the free vibration characteristics. As a main result of the present paper is this fact that the lowest frequencies are obtained for phi(0) = h(0)/l(0) = 0.6. It is concluded that with increase of phi(0) from small values, the mass is increased more than increase of stiffness that leads to a decrease in frequencies unlike higher values of phi(0), in which an increase in structural stiffness is reached respect to a small increase in mass that leads to a main increase in frequencies.