This paper presents a novel numerical method for simulating local scouring around bridge piers using a three-dimensional free-surface RANS turbulent flow model. Strong turbulent fluctuations and the down-flows around the bridge pier are considered important factors in scouring the bed. The turbulent kinetic energy transported to the bed due to the strong vertical flow is approximated and converted to a shear stress to entrain sediment particles from the bed in addition to the conventional bed shear stress. A non-equilibrium bed load transport approach is used to model the erosion and sediment transport processes. The hydrodynamic model is validated using experimental data with a fixed flat bed and a scour hole. The local scour model is validated using four sets of experimental data of clear water scour and live-bed scour cases. Steady and unsteady flow conditions and uniform and non-uniform sediment conditions are included. Agreement between the simulations and the measured data is demonstrated.