We propose a new turbulence model which is modified from the low-Reynolds-number k-ε model developed by Nagano and Tagawa. The main improvement is made by the introduction of the Kolmogorov velocity scale, u_ε≡(νε)^1/4, instead of the friction velocity uτ, to account for the nearwall and low-Reynolds-number effects. We have also reevaluated the model constants in the transport equations of the turbulent energy and its dissipation rate. With these modifications, it is shown that the present model predicts quite successfully a diffuser flow with a strong adverse pressure gradient and the separating and reattaching flows downstream of a backward-facing step.