We show from a series of molecular dynamics simulations that the tensile fracture behavior of a nanocrystalline graphene (nc-graphene) nanostrip can become insensitive to a pre-existing flaw (e.g., a hole or a notch) below a critical length scale in the sense that there exists no stress concentration near the flaw, the ultimate failure does not necessarily initiate at the flaw, and the normalized strength of the strip is independent of the size of the flaw. This study is a first direct atomistic simulation of flaw insensitive fracture in high-strength nanoscale materials and provides significant insights into the deformation and failure mechanisms of nc-graphene.