For simulating high Reynolds flows around bridge decks effectively, as well as expanding the application of the lattice Boltzmann method (LBM) in bridge wind resistance, dynamic Smagorinsky sub-grid-scale model was embedded into the multiple relaxation times (MRT) formulation of LBM. The subgrid eddy viscosity can be obtained from performing discrete filtering operations at lattice grid and test-filter levels. Grid filter was locally calculated by means of non-equilibrium moments of the MRT-LBM, while test filter was computed by finite difference method at a larger scale. A MRT-LBM-DSM method, which can simulate high Reynolds flows effectively, was constructed through modifying the kinematic viscosity of the MRT-LBM by incorporating subgrid eddy viscosity. As an example, the Sutong bridge was investigated to calculate its static force coefficients and aerodynamic derivatives. The comparison between simulation and experimental results showed that the present method gives much better prediction of turbulent flows, and can be used for simulating high Reynolds flows around bridge decks and calculating aerodynamic parameters.