An unsteady numerical simulation was performed for locally-forced separated and reattaching flow over a backward-facing step. The local forcing was given to the separated and reattaching flow by means of a sinusoidally oscillating jet from a separation line. A version of the $k-{varepsilon}-f_{mu}$ model was employed, in which the near-wall behavior without reference to distance and the nonequilibrium effect in the recirculation region were incorporated. The Reynolds number based on the step height (H) was fixed at $Re_H=33000$, and the forcing frequency was varied in the range $0{leq}St_H{leq}2$. The predicted results were compared and validated with the experimental data of Chun and Sung. It was shown that the unsteady locally-forced separated and reattaching flows are predicted reasonably well with the $k-{varepsilon}-f_{mu}$ model. To characterize the large-scale vortex evolution due to the local forcing, numerical flow visualizations were carried out.