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Magnetic resonance electrical impedance tomography is an imaging modality which reconstructs true conductivity images by using current density distribution and surface potential measurements. In this study, two current based algorithms, namely equipotential projection  and J-substitution image reconstruction  algorithms are compared. A novel reconstruction technique, J-substitution and equipotential-projection based hybrid reconstruction algorithm, is proposed. In this technique, the image which is reconstructed with equipotential projection algorithm is assigned as the starting conductivity distribution for J-substitution algorithm. Moreover, true conductivity values can be reconstructed with two surface potential measurements. Simulation results on a thorax phantom show that the proposed method has a better performance in some regions.