Magnetic resonance electrical properties tomography (MR-EPT) maps the spatial distribution of the patient's electrical conductivity and permittivity using the measured B1 data in a magnetic resonance imaging (MRI) system. Existing MR-EPT methods are usually not clinically accessible owing to their technical limits such as strong noise sensitivity. In this study, we develop a new MR-EPT method that re-expresses the involved differential equations (DEs) based on the divergence theorem. In comparison with traditional methods, the proposed method avoids the grid-wise computation of the second-order derivatives of B1+ , thereby improving the robustness against noise. Besides, for applications where the structural information can be determined in advance, EPs of a region of interest (ROI) can be calculated in a fast and efficient manner. The proposed method is firstly validated with numerical simulations, in which a three-block phantom and an anatomically accurate Duke Head model are used to evaluate the proposed method. Experiments on the 9.4T MRI system were then conducted to validate the simulations. Both results indicated that the proposed MR-EPT solution could provide a more robust reconstruction of electrical properties maps compared with conventional methods.