Graphene/metal matrix composites have attracted intense interest because of superior mechanical properties, while introducing graphene into the nanotwinned metal matrix has been rarely studied. Here, a nanolayered composite is constructed by introducing single-layer graphene sheets into the nanotwinned Cu (nt-Cu) matrix. The shock response of the composite is investigated using molecular dynamics simulations. Compared to nt-Cu and single-crystal Cu, the graphene/nt-Cu composite possesses higher shock resistance and better self-healing ability simultaneously. It is found that the wrinkling of graphene can act as an initiator for rapid nucleation of numerous dislocations in the composite at the impact velocity of 4.5 km/s, while only an elastic wave is observed in the metal matrix under the same conditions. The subsequent propagation of dislocations effectively absorbs the impact force, leading to a rapid decline of shock stresses and particle velocities. There is a synergistic effect between graphene and twin boundaries on increasing the plastic sensitivity of the composite at a higher impact velocity, resulting in the larger dislocation density with higher shock resistance. Moreover, a fast and smooth self-healing process is observed with the propagation of the reflected wave. As graphene cannot be easily perturbed by dislocations due to high in-plane stiffness, the integrity of the crystal lattice in the graphene/nt-Cu composite is slowly degraded with a better self-healing performance.