We present two‐dimensional computer simulation results of magnetic vortex systems driven by Lorentz force through polycrystalline superconductors with random network structures of twin boundaries. Langevin dynamics simulations of a point vortex model demonstrate that (1) the threshold behavior of I‐V curves is observed, and (2) the threshold current is a decreasing function of an average superconducting grain size. © 2004 American Institute of Physics