We present a numerical model for the simulation of 3D sediment transport in a Newtonian flow with free surfaces. The Navier-Stokes equations are coupled with the transport, deposition, and resuspension of the particle concentrations, and a volume-of-fluid approach to track the free surface between water and air. The numerical method relies on operator splitting to decouple advection and diffusion phenomena, and a two-grid method. An appropriate combination of characteristics, finite volumes, and finite elements methods is advocated. The numerical model is validated through comparisons with numerical experiments, sediment flushing, shear flow erosion, and the formation of dunes.