This study develops an ordinary state-based peridynamic coarse-graining (OSPD-CG) model for the investigation of fracture in single-layer graphene sheets (SLGS), in which the peridynamic (PD) parameters are derived through combining the PD model and molecular dynamics (MD) simulations from the fully atomistic system via energy conservation. The fracture failure of pre-cracked SLGS under uniaxial tension is studied using the proposed PD model. And the PD simulation results agree well with those from MD simulations, including the stress–strain relations, the crack propagation patterns and the average crack propagation velocities. The interaction effect between cracks located at the centre and the edge on the crack propagation of the pre-cracked SLGS is discussed in detail. This work shows that the proposed PD model is much more efficient than the MD simulations and, thus, indicates that the PD-based method is applicable to study larger nanoscale systems.