Electrical conductivity is a passive material property primarily determined by concentrations of charge carriers and their mobility. The macroscopic conductivity of biological tissue at low frequency may exhibit anisotropy related with its structural directionality. When expressed as a tensor and properly quantified, the conductivity tensor can provide diagnostic information of numerous diseases. Imaging of conductivity distributions inside the human body requires probing it by externally injecting conduction currents or inducing eddy currents. Here we propose a novel method to reconstruct conductivity tensor images using an MRI scanner without any current injection.