This study develops a novel rough-wall model for large eddy simulation (LES) based on recent work on wall-modelled LES. This approach is capable of solving for the basic flow character over a rough wall at high Reynolds numbers without resolving the details of the roughness elements. The wall-modelled LES approach on a smooth wall is proven to be sufficiently precise to predict the velocity profile and wall shear stress. The average roughness shear stress can be combined with the smooth-wall shear stress in the inner-layer wall model by defining a roughness shear stress ratio α. The instantaneous shear stresses caused by the roughness elements are calculated by the pressure projection and elevation fields. The total shear stress is fed back to the outer-layer LES mesh as a new boundary condition. The results of the wall-modelled LES correspond well with the experimental data. The comparison between the simulation and experiment reveals that the wall-modelled LES approach presented in this research is capable of predicting the flow in a rough-wall boundary layer without resolving the detailed roughness element geometries.