Large-eddy simulation (LES) with non-equilibrium dynamic wall-model is applied to a subsonic flow over an airfoil near stall condition at high Reynolds number (chord based Rec = 2.1×106) to investigate the predictability of the wall-modeled LES for the transitional and separated flow. The wall model considered in this study is built based on the recent wall-model developments by Kawai and Larsson [Phys. Fluids 24 015105, 2012; and Phys. Fluids accepted (to appear), 2013] and is extended to the transitional and separated flow by introducing a transition treatment in the wall model. Comparisons between the non-equilibrium wall model and equilibrium model illustrate the importance of involving the non-equilibrium effects into the wall model. By incorporating the non-equilibrium effects, the wall-modeled LES yields accurate resolved turbulence, both in terms of statistics and structures.