The cylindrical sandwich shells with auxetic 3D double-V meta-lattice core and functionally graded (FG) GRC (graphene-reinforced composite) facesheets are designed, modeled and analyzed to reveal their nonlinear dynamic response when subjected to low-velocity impact. The 3D double-V meta-lattices, developed from the 2D double arrowed honeycombs, are further self-adapted to meet the requirements of the curved space between facesheets of sandwich shells. By means of micromechanical modeling according to the extended Halpin-Tsai model, the temperature-dependent properties are determined for GRC facesheets, which are further designed to possess FG configurations along the radical direction of the shell structures. Full-scale FE modeling and nonlinear dynamic analysis are then carried out. Numerical results reveal the novelty of FG configurations of GRC facesheets, and include the effects of drop-heights, shell lengths, strut radii, shell radii and thermal environments. Present models, including 3D meta-lattice cores and polymer matrix composite facesheets, are believed to provide new thoughts for the design of lightweight sandwich shells and their applications in the fields of ocean engineering. •The 3D double-V meta-lattices are adapted to meet the curvature variation of the cylindrical sandwich shells.•The GRC facesheets are designed to possess FG configurations.•Thermal effects are taken into account, and material properties are assumed to be temperature-dependent.•The effects of curvature radii are revealed to be significant, both on contact forces and displacements.