Abstract: The improvement on the lattice Boltzmann method enables the Entropic Lattice Boltzmann Method (ELBM) to obtain the potential in order to simulate high Reynolds number turbulence stably. A renormalization group subgrid scale turbulence model for Large Eddy Simulation (LES) is introduced into the ELBM. Based on ELBM, a renormalization group subgrid scale model and the standard Smagorinsky subgrid scale model for LES are established simultaneously. Simulation of high Reynolds number turbulent flow around a circular cylinder is then carried out. It is concluded that the established renormalization group subgrid scale model for LES based on ELBM is effective for the simulation method with high Reynolds number turbulence, which is seen to be slightly better than the standard Smagorinsky subgrid scale model.