We performed molecular dynamics (MD) simulations to investigate the mechanical properties of polycrystalline graphene. By constructing molecular models of ultra-fine-grained graphene structures, we studied the effect of different grain sizes of 1-10 nm on the mechanical response of graphene. We found that the elastic modulus and tensile strength of polycrystalline graphene decrease with decreasing grain size. The calculated mechanical proprieties for pristine and polycrystalline graphene sheets are found to be in agreement with experimental results in the literature. Our MD results suggest that the ultra-fine-grained graphene structures can show ultrahigh tensile strength and elastic modulus values that are very close to those of pristine graphene sheets.