A transient three-dimensional (3D) coupled mathematical model has been established to study the desulfurization behavior in electroslag remelting (ESR) process. The solutions of the mass, momentum, energy, and species conservation equations were simultaneously calculated by the finite volume method. The Joule heating and Lorentz force were fully coupled through solving the Maxwell's equations with the assistance of the magnetic potential vector. The movement of the metal droplet was described by the volume of fluid (VOF) approach. In order to include the influences of the slag composition and the electric current on the desulfurization, a thermodynamic and kinetics module was introduced. An experiment was conducted to validate the model. The completely comparison between the measured and simulated data indicates that the model can predicate the desulfurization with acceptable accuracy. The sulfur in the metal would be mainly transferred into the slag in the formation of the droplet. After the droplet enters into the metal pool, the sulfur would fast expand to the rest of the slag pool and move to the outer side of the mold along with the metal, and finally flows downward. The maximum calculated removal ratio during the whole process can reach up to 71%. (C) 2016 Elsevier Ltd. All rights reserved.