In order to perform Implicit Large Eddy Simulation (ILES) on complex geometries at high Reynolds numbers, a wall model based on the simplified Thin Boundary Layer Equations (TBLE) is designed in the framework of ILES with a cut-cell finite-volume immersed boundary method. This wall model is validated for turbulent channel flow at friction Reynolds number up to Reτ = 2,000 on very coarse grids. The results compared with DNS and LES without wall model show that the wall model has the potential to improve the mean velocity in the outer flow region well at high Reynolds number. The wall model is applied to a complex converging diverging channel flow at Reynolds number Re = 7,900 on very coarse meshes. Improved mean velocities and Reynolds stresses are obtained, which shows that the wall model has the ability to perform ILES on complex geometries at high Reynolds numbers.