Magnetic resonance electrical impedance tomography (MREIT) has been developed as a new medical imaging modality providing high-resolution conductivity and current density images. This paper is about MREIT of the breast. To show the feasibility of breast MREIT, we carried numerical simulations and breast phantom experiments. We found that an anomaly with 4 mm diameter can be visualized in a reconstructed conductivity image using 5 mA injection current if the SNR of the corresponding MR magnitude image is at least 150. We propose a desirable electrode configuration and show our first experimental results of the breast MREIT. Developing an RF coil for the breast MREIT, we plan to conduct various experimental studies including tissue phantoms.