A dynamical model, based on the Lattice Boltzmann method, is presented for simul ating the two-dimensional moving elliptic cylinders in a Newtonian fluid. Using this model, we have simulated the motions of elliptic cylinders with different shapes in a Newtonian fluid under the same initial conditions, and the motions o f an elliptic cylinder under different initial conditions. The numerical simulat ions are compared with the results of moving cylinders under the same conditions . The characters of the two-dimensional moving elliptic cylinders are discussed, and some new results are obtained.