To calculate complex turbulent flows with separation and heat transfer, we have developed a new turbulence model for flow field, which is modified from the latest low-Reynolds-number k-epsilon model. The main improvement is achieved by the introduction of the Kolmogorov velocity scale, u(epsilon) = (nuepsilon)1/4, instead of the friction velocity u(tau), to account for the near-wall and low-Reynolds-number effects in both attached and detached flows. The present model predicts quite successfully the separating and reattaching flows downstream of a backward-facing step, which involve most of the essential physics of complex turbulent flows, under various flow conditions. We have also discussed in detail the structure of the separating and reattaching flow based on the computational results, and presented several important features closely related to the mechanism of turbulent heat transfer.