The fatigue failure of graphene plays an important role in determining the service life of many graphene-based nanodevices. In this paper, the fatigue behaviours of polycrystalline graphene are investigated by using molecular dynamics (MD) simulations. The results show that the fatigue process of polycrystalline graphene contains three stages, which, successively, are the initiation of microvoids, formation of large cracks and rapid propagation of cracks. The loading amplitude, grain size and temperature can greatly affect the fatigue properties. Evolutions of the mechanical and thermal transport properties of polycrystalline graphene during the fatigue process are also investigated by MD simulations. No significant changes are found in these material properties in the first two stages of fatigue. However, a dramatic decrease in the Young's modulus, tensile strength and thermal conductivity is found in the last stage. The large cracks occurring in the last stage are responsible for the reduced Young's modulus and tensile strength, because they can reduce the effective stiffness of polycrystalline graphene and induce the stress concentration in graphene. Meanwhile, large cracks also can reduce the heat flux and, meanwhile, increase the phonon scattering in polycrystalline graphene, both of which account for the reduced thermal conductivity observed in the last stage of fatigue.