Abstract: The lattice Boltzmann method (LBM) is used to simulate the incompressible flow past a transversely oscillating circular cylinder. Simulations are conducted at Reynolds number Re=185. The results show that as the oscillation frequency of the cylinder is increased relative to the natural vortex shedding frequency of the corresponding stationary cylinder, the initially formed concentration of vorticity moves closer to the cylinder until a limiting position reaches. At this point, the vorticity concentration abruptly switches to the opposite side of the cylinder. When the oscillation frequency is near the natural vortex shedding frequency of a corresponding stationary cylinder, frequency synchronization occurs. When the oscillation frequency is away from the natural vortex shedding frequency, frequency synchronization also disappears. In several subharmonic and superharmonic excitation situations, vortex shedding frequency in the near wake region also equals to the natural one of the corresponding stationary cylinder.