Magnetic induction tomography ( MIT) can be used to probe electrical conductivity variation of an object. It offers a nondestructive and contactless means of imaging the internal conductivity distribution of the object. The forward problem in MIT is a general eddy current problem, which is required to estimate the measured data for a given conductivity distribution. The edge finite-element method with a formulation using a magnetic vector potential has been implemented to solve the forward problem. Conductivity reconstruction in MIT is a nonlinear and ill-posed inverse problem. The regularization techniques are required to incorporate a priori knowledge of the conductivity distribution for a stable solution of this inverse problem. This article presents a conductivity interface reconstruction technique, which has an inherent regularization property. Instead of calculating the conductivity distribution in the whole region of interest, the interface between two different conductivities is reconstructed. A narrowband level-set method has been implemented to describe the interfaces. An iterative optimization scheme has been used to modify the interface estimation in each iteration step, so that the predicated forward solution is closed to the measured data. The results are presented using experimental data representative of an application of MIT in molten metal flow visualization.