The objective of our research is to improve the image reconstruction method for the static impedance imaging used in electrical impedance tomography (EIT). The multigrid (MG) method is implemented to speed up the forward problem in EIT. Compared with the direct solution methods and other iterative algorithms, it is more efficient, especially for large system models. On the other hand, due to the nonlinearity of the underlying problem, all existing methods suffer from local optima. In order to find global optima or at least near optima, simulated annealing (SA) is used, for the first time, to solve the inverse problem of EIT. Some strategies are also proposed, including the insertion of solving the forward problem in the annealing process and the discretization technique of the configuration space. The simulation experiments show the advantages and feasibility of the proposed method.