A three-dimensional (3D) computational fluid dynamics (CFD) model is used to calculate the scour and the deposition pattern around a pier for two different boundary conditions: constant discharge and regular waves. The CFD model solves Reynolds-Averaged Navier–Stokes (RANS) equations in all three dimensions. The location of the free-surface is represented using the level-set method (LSM), which calculates the complex motion of the free-surface in a very realistic manner. For the implementation of waves, the CFD code is used as a numerical wave tank. For the geometric representation of the moveable sediment bed, the LSM is used. The numerical results for the local scour prediction are compared with physical experiments. The decoupling of the hydrodynamic and the morphodynamic time step is tested and found to be a reasonable assumption. For the two situations of local pier scour under current and wave conditions, the numerical model predicts the general evolution (geometry, location, and maximum scour depth) and time development of the scour hole accurately.