In electrical impedance tomography (EIT), different currents are applied to electrodes on the surface of an object and the resulting voltages are measured. The image of impedance (resitivity, conductivity) distribution or changes in the object is reconstructed based on these boundary measurements. EIT is a functional imaging technique, which may reveal the physiological and pathological information by human body's impedance properties. The advantages such as the non-invasive modality and the relative low cost make EIT become a research hot in medical imaging. However, the image reconstruction in EIT is a high ill-posed, non-linear, inverse problem, and it becomes a key and difficult point in EIT. In dynamic EIT, the image of impedance changes in the object is reconstructed. On the other hand, the image of impedance distribution in the object is reconstructed in static EIT, which is more difficult than in dynamic EIT. We study the reconstruction of static EIT in this paper, due to the static EIT has better clinical application prospect than the dynamic EIT.