A large-eddy simulation study has been undertaken to investigate the turbulent structure of open-channel flow over three-dimensional (3D) dunes. The governing equations have been discretized using the finite volume method, with the partial cell treatment being implemented in a Cartesian grid form to deal with the 3D dune topography. The simulated free surface elevations, mean flow velocities and Reynolds shear stress distributions have been compared with experimental measurements published in the literature. Relatively close agreement has been obtained between the two sets of results. The predicted mean velocity field and the associated turbulence structure are significantly different from those observed for flows over two-dimensional dunes. The effects of dune three-dimensionality are reflected in spanwise variations of mean flow fields, secondary currents and different distributions of vertical profiles of the double-averaged velocity. Furthermore, large-scale vortical structures, such as spanwise rollers and hairpin-like structures, are predicted in the simulations, with most of them being generated in the concave regions of the 3D dunes.