In order to understand the movement of the inclusion in electroslag remelting (ESR) process, a transient three-dimensional (3D) comprehensive mathematical model has been established. The finite volume method was employed to solve the mass, momentum and energy conservation equations as well as the Maxwell's equations. The volume of fluid (VOF) approach was used to define the redistribution of the metal and the slag. The inclusion trajectory was described by using the two-way coupled EulerLagrange method. Experiments were conducted to verify the proposed model. The removal ratios of the inclusions with 1 gm and 10 gm diameters constantly increase with a larger current. The removal ratios of the inclusions with 3 mu m and 5 gm diameters first increase with the current ranging from 1000 A to 1600 A, but then decrease if the current continuously increases to 1800 A. The inclusions with 15 gm and 20 gm diameters are almost completely eliminated in the five currents. The increase of the inclusion density would reduce the removal ratio of the inclusion with a larger diameter in different degrees. (C) 2018 Elsevier Ltd. All rights reserved.