Applies multiple relaxation lattice Boltzmann and large eddy simulation of dynamic Smagorinsky model for simulating turbulent flow around a cylinder, and researches periodic change of turbulent vortex flow around a cylinder under different Re 300~10 000. The research shows that: the calculated Strouhal numberand the drag coefficient are consistent with the published experimental results and the finite element simulation results, indicating that the method is reasonable for simulating turbulent flow of different Reynolds number .