This paper briefly introduces how to apply Monte Carlo simulations to non-equilibrium dynamic systems. Non-equilibrium systems have been observed at almost all levels of natural and manmade systems,which are characterized by non-zero continuous traffic currents.Totally asymmetric simple exclusion process (ASEP)has been regarded as a paradigm for modeling and simulation of such non-equilibrium systems.Monte Carlo simulations for the normal TASEP have been illustrated.Some possible extensions of TASEP have been presented.All TASEP models can be simulated using Monte Carlo methods.Some interesting physical phenomena such as spontaneous symmetry breaking spontaneous symmetry breaking finite-size effect and flipping process have been observed via Monte Carlo simulations.Spontaneous symmetry breaking and finite-size effect have been discussed in detail.More careful Monte Carlo simulations are suggested to confirm the finite-size effect argued in the literature.