An improved version of nonlinear low-Reynolds-number k-epsilon model is developed. In this model, the limiting near-wall behavior and nonlinear Reynolds stress representations are incorporated. Emphasis is placed on the adoption of R(y) (=k(1/2)y/v) instead of y(+) (=u,y/v) in the low-Reynolds-number model for predicting turbulent separated and reattaching flows. The non-equilibrium effect is examined to describe recirculating flows away from the wall. The present model is validated by doing the benchmark problem of turbulent flow behind a backward-facing step. The predictions of the present model are cross-checked with the existing measurements and DNS data. The model performance is shown to be generally satisfactory.