Development of a reliable and accurate predictive model for the melting performance of the Joule-heating ceramic melter (JHCM) to vitrify the high-level liquid waste (HLLW) is quite crucial to safely and efficiently treat HLLW. However, due to the harsh operating conditions of HLLW vitrification, such as high temperature and high radiation, the physical field information and melting performance of the melter are not fully understood. Therefore, this work applied the GFM (Glass Furnace Model) software and numerical simulation technique to analyze the melting performance of a JHCM for HLLW vitrification under different electrode connection modes. The influences of electrode connection modes on mass transfer, heat transfer, glass flow behavior, and the distribution of various physical fields in the melter were carefully investigated. The results indicate that during standard operation, the average temperature of the glass melt is ~1 160 ℃, the average Joule heat is ~120 kW/m³, and the melting efficiency is ~0.004 kg/(m²·s). Compared to normal operation, the melter would still be able to work, when the electrodes are misaligned, but the distribution of Joule heat in the melt is uneven and the glass melt flow circulation is loose and weak, which are not beneficial for glass melting and homogenization. In this case, the risk of electrode damage will significantly increase as well.