Abstract: The dynamic snap-through and oscillation behaviors are studied of a post-buckled functionally graded graphene reinforced composite (FG-GRC) beam with a viscoelastic core under low-velocity impact. The modified Halpin Tsai meso-mechanical model is used to predict the material properties of FG-GRC. The Hertz point contact model is used to calculate the contact force between the impactor and the post-buckled beam. Considering the axial prestress, the constitutive relations of the composite layer and the Kelvin type viscoelastic constitutive model of the damping layer are proposed. A generalized higher-order shear deformation zig-zag beam theory is utilized to model the nonlinear displacement fields. Based on the Hamilton energy variational principle, the governing equations of dynamics are derived. Through two-step analysis, the post-buckling equilibrium paths are obtained as the initial state condition for the impact problem analysis. Further, combined with the fourth-order Runge Kutta method, the two-step perturbation-Galerkin method is extended to simulate the time history curves of the contact force and the dynamic response curves of the post-buckled beams. Compared with the results based on other beam models, the correctness of the material model, theoretical model and computation method is validated. The dynamic characteristics of bi-stable large amplitude vibration of the post-buckled beams under single and two collisions are studied. The effects of axial load, impact velocity, viscoelastic damping characteristics and impactor materials on the contact force and the deflection time history curves of the post-buckled beams are discussed. The results suggest that the contact force is only sensitive to the impact velocity. A certain structural collision parameter design can change the response of the post-buckled beam from single potential energy trap motion to double trap large oscillation, and the contact force is approximately unchanged. The results of this work can be of reference significance for the design of bi-stable energy capture system with collision.