Abstract: A slip-wall model is combined with the immersed boundary method for large-eddy simulation of flows with complex geometries. Firstly, large eddy simulation of flows over periodic hills are conducted to evaluate the effects of the tangential pressure gradient in wall model. Both the equilibrium stress balance model which based on the assumption of an equilibrium boundary-layer and the non-equilibrium wall model, in which the pressure gradient blend into the simplified thin boundary-layer equations and the RANS-like eddy viscosity in both the procedure of computing the wall-shear stress and reconstructing the wall-slip velocity, are utilized for comparison. The numerical results show that the pressure coefficient is not sensitive to the types of wall model which we considered, especially the strong pressure gradient in front of the hill crest is well catched by both models. However, when taking into account the tangential pressure gradient, the non-equilibrium wall model is superior to the equilibrium one for its ability to improve the prediction of the wall-shear stress and flow separation. When the equilibrium stress balance model is used, the wall-shear stress is heavily under-predicted and remarkable discrepancies of the mean velocity profiles can also be seen in the recirculation region. By comparison, the correction of the non-equilibrium wall model is proportional to both the tangential pressure gradient and the normal distance away from the wall, thus the hydrodynamic coefficients and the mean flow statistics are all in good agreement with the references even on very coarse grids. Secondly, large-eddy simulation of flow around an axisymmetric body is conducted to assess the applicability of current method when applied to high Reynolds number wall-bounded turbulent flows. The flow structures and the hydrodynamic characteristics are well predicted by the non-equilibrium wall model. This work confirms that the immersed boundary method in combination with the non-equilibrium slip-wall model is a possible and promising way to deal with turbulent flows which have complex geometries.