Understanding the interaction between void and grain boundary (GB) is important to the design of radiation resistant materials by GB engineering and to achieve high quality metallurgical diffusion joining. In this study, the interaction between nano-voids and GBs has been systematically investigated by molecular dynamics simulations. The bicrystal Cu sample was used throughout the work, and the dynamic GB-void interaction was achieved by GB migration under shear deformation. Both high-angle GBs (Σ5 (310) GB, Σ5 (210) GB) and low-angle GBs (Σ37 (750) GB, Σ61 (650) GB) were investigated, and the effect of void size and temperature on the simulation result was examined. The transition of the deformation mechanism from GB migration to dislocation propagation was observed during the interaction between voids and high-angle GBs at low temperature (T = 10 K). At higher temperature (T = 300 and 600 K), the migrating GB can be pinned to voids, freely traversed voids, or dissolved voids in the process of their interaction. The void-drag effect on GB motion was analyzed based on the Zener-like equation, which indicates that the retarding pressure applied to the migrating GB by a void is closely related to the surface area of the void, the degree of contact between GB and void, and GB energy. By investigating the thermal stability of a void at the stationary GB, it was found that the dissolution of voids at a moving GB cannot be attributed solely to the thermal diffusion mechanism. The dynamic migration of high-angle GBs can significantly accelerate the dissolution time of the void. Atomistic analysis indicated that the migrating GB rearranged the atoms on the void surface by the collective motion of structural units, and the GB structural phase transformation provided an efficient diffusion channel for transporting the vacancies. The low-angle GBs show a reduced ability to dissolve the voids than the high-angle GBs, which can be ascribed to their low GB energy and diffusion coefficient, the fast GB migration velocity, and the discrete GB structure.