Modeling of the three phase electric arc furnace and its voltage flicker mitigation are the purposes of this paper. For modeling of the electric arc furnace, at first, the arc is modeled by using current-voltage characteristic of a real arc. Then, the arc random characteristic has been taken into account by modulating the ac voltage via a band limited white noise. The electric arc furnace compensation with static VAr compensator, Thyristor Controlled Reactor combined with a Fixed Capacitor bank (TCR/FC), is discussed for closed loop control of the compensator. Instantaneous flicker sensation curves, before and after accomplishing compensation, are measured based on IEC standard. A new method for controlling TCR/FC compensator is proposed. This method is based on applying a predictive approach with closed loop control of the TCR/FC. In this method, by using the previous samples of the load reactive power, the future values of the load reactive power are predicted in order to consider the time delay in the compensator control. Also, in closed loop control, two different approaches are considered. The former is based on voltage regulation at the point of common coupling (PCC) and the later is based on enhancement of power factor at PCC. Finally, in order to show the effectiveness of the proposed methodology, the simulation results are provided.