At present, the SingleInput SingleOutput (SISO) HammersteinWiener (HW) model is widely used for singlephase electrode system in Alternating Current (AC) Electric Arc Furnace (EAF). This kind of model simplifies the true structure of the electrode system, which results in the low prognostics accuracy. To solve this problem, a MultiInput MultiOutput (MIMO) HW model for electrode system is proposed in this paper. Due to the model structure is the same with the practical electrode system, the prognostics results can be enhanced. Under the condition that the MIMO static nonlinear block is irreversible, a parameter identification method of MIMO HW model is presented based on the separable nonlinear least square algorithm. Finally, the prognostics accuracy of the proposed model is proved to be higher than the traditional SISO model by using the practical data.