Polycrystalline graphene nanoribbons usually experience a brittle rupture before failure, and the irreversible breaking occurs in grain boundaries (GBs). In this paper, molecular dynamic simulations are conducted to study the fatigue properties of bi-crystal graphene nanoribbons under a periodic in-plane compression. It is found that ribbon edges rather than GBs dominate the dynamic stability when the ribbon width is smaller than 5 nm. The fatigue failure is closely related to the misorientation angle between two grains because of the distinct edge energy. It always starts from the edges with higher energy and results in a localized damage at the edges.