In order to improve understanding the melt convection in an electro-fused magnesia furnace, a three-dimensional finite-element method based model of the furnace is presented. Electromagnetic stirring and buoyancy effects are both considered in three typical cases with different bath sizes. Dimensionless parameters including Reynolds number, Richardson number, and Prandtl number are adopted to characterise the melt convection. The Reynolds number indicates that the convection is fully turbulent in the three cases, and the numerical results reveal that the flow and temperature fields are both significantly influenced by the line current. According to the calculated Richardson number, neither nature nor forced convection is negligible in all cases. The buoyancy becomes more crucial when the bath volume grows and the current decreases, and the magnetic stirring becomes more crucial when the bath volume shrinks and the current increases. The quantitative analysis of the line resistance of the bath indicates that it is more easily influenced by the bath radius than the bath height.