In order to predict the local scour hole and its evaluation around a cylindrical bridge pier, the computational fluid dynamics (CFD) and theories of sediment movement and transport were employed to carry out numerical simulations. In the numerical method, the time-averaged Reynolds Navier-Stokes equations and the standard k-e model were first used to simulate the three-dimensional flow field around a bridge pier fixed on river bed. The transient shear stress on river bed was treated as a crucial hydrodynamic mechanism when handling sediment incipience and transport. Then, river-bed volumetric sediment transport was calculated, followed by the modification of the river bed altitude and configuration. Boundary adaptive mesh technique was employed to modify the grid system with changed river-bed boundary. The evolution of local scour around a cylindrical bridge pier was presented. The numerical results represent the flow pattern and mechanism during the pier scouring, with a good prediction of the maximum scour hole depth compared with test results.