The first molecular dynamics (MD) study was conducted to explore mechanical-failure response of ultra-fine grained single-layer boron-nitride films. We used MD simulations to construct relatively large molecular models of polycrystalline structures with random grain configurations. By applying uniaxial tensile loading, we then studied the grain size effect on the mechanical response of polycrystalline boron-nitride nanosheets. Our results reveal that by decreasing the grain size, the elastic modulus of polycrystalline films decreases gradually. Interestingly, our MD results reveal that ultra-fine grained samples could present a tensile strength of around half that of the pristine films. Our investigation suggests that experimentally fabricated polycrystalline boron nitride nanosheets can exhibit remarkably high mechanical properties.