A new k-epsilon-f(mu) turbulence model is proposed, in which the near-wall effect without reference to distance and the nonequilibrium effect are incorporated. Ln this model, the non-local near-wall effect in a general coordinate system is taken into account by the f(mu) equation, and the local anisotropy in strongly strained turbulent flows is introduced in the epsilon equation. The near-wall characteristics of the present model are ascertained from the DNS data. Also, the validation is explored to separate and reattaching flows. The backward-facing step flow is selected for benchmark test of the present model and the response of the model to flows involving complex surfaces is assessed. The predictions of the present model are checked with the existing measurements. The model performance is shown to be generally satisfactory.