We have investigated induced current magnetic resonance electrical impedance tomography (IC-MREIT) by means of computer simulations. The J-substitution algorithm was implemented to solve the IC-MREIT reconstruction problem. By providing physical insight into the charge accumulating on the interfaces, the convergence characteristics of the reconstruction algorithm were analyzed. The simulation results conducted on different objects were well correlated with the proposed theoretical analysis. The feasibility of IC-MREIT to reconstruct the conductivity distribution of head-brain tissues was also examined in computer simulations using a multi-compartment realistic head model. The present simulation results suggest that IC-MREIT may have the potential to become a useful conductivity imaging technique.