A novel MR-EIT imaging modality has been developed to reconstruct high-resolution conductivity images with true conductivity value. In this new technique, electrical impedance tomography (EIT) and magnetic resonance imaging (MRI) techniques are simultaneously used. Peripheral voltages are measured using EIT and magnetic flux density measurements are determined using MRI. The image reconstruction algorithm used is an iterative one, based on minimizing the difference between two current density distributions calculated from voltage and magnetic flux density measurements separately. The performance of the proposed method and the suggested reconstruction algorithm are tested on simulated data. A finite element model with 1089 nodes and 2048 triangular elements is used to generate the simulated potential and magnetic field measurements. A 16 electrode opposite drive EIT strategy is adopted. The spatial resolution is space independent and limited by either the finite element size or half the MR resolution. The worst of the two defines the spatial resolution. The rms error in reconstructed conductivity for a concentric inhomogeneity is calculated as 5.35% and this error increases to 13.22% when 10% uniformly distributed random noise is added to potential and magnetic flux density measurements. The performance of the algorithm for more complex models will also be presented.