It is generally believed that initial geometric imperfection has a significant impact on the nonlinear dynamic behavior of structures. However, the mechanism that the initial geometric imperfection affects the nonlinear internal resonance behavior of axially moving conical shells is still unclear. To answer this question, the 1∶2 internal resonance behavior of graphene platelets reinforced metal foam (GPLRMF) conical shells with initial geometric imperfection and axial motion is studied in this paper. Firstly, based on the Reddy high-order shear deformation theory and von Karman geometric nonlinearity, the motion equation of the conical shell is derived. Then, considering the first two vibration modes and discretizing the motion equation through the Galerkin principle. Subsequently, the multi-scale method is used for solving, and the internal resonance dynamic response curves of the conical shell under the first two vibration modes are obtained through numerical calculations. Finally, the motion bifurcation and chaotic dynamic behavior under 1∶2 internal resonance conditions are studied using the Runge-Kutta method.