A k-ε turbulence model is developed to calculate wall turbulent shear flows under various pressure gradient conditions. In the present model, we set the dissipation rate of turbulent energy at a wall equal to zero, though the wall limiting behavior of velocity fluctuations is reproduced exactly. Thus, the model assures computational expediency and convergence. The proposed model is constructed to properly take into account the effects of pressure gradients on shear layers. It was found by Nagano et al. (1992) that in adverse pressure gradient flows the Van Driest damping constant decreased with increasing dimensionless pressure gradient parameter P+. Therefore, the present model has introduced the modified Van Driest damping function which is a function of P+. The proposed model was tested by application to a turbulent channel flow and boundary layers with P+ < 0, P+=0 and P+ > 0. The model predictions indicate that agreement with the experiment and the direct simulation data is very good over a wide range of pressure variations.