Electrical impedance tomography (EIT) is an imaging technology that offers the advantages of being noninvasive, and it does not generate ionizing radiation. The main difficulty in applying EIT is to solve an ill-posed nonlinear inverse problem. Given a set of electrical voltages measured at the surface of a volume conductor, the goal is to identify the materials that are present in the domain by determining their electrical conductivities. However, since EIT is a nonlinear problem, various algorithms proposed in the literature can only approximate real conductivity distributions. Nonlinear algorithms, especially artificial neural networks (ANNs), have been proposed to solve this inverse problem, but these algorithms are usually limited by slow convergence issues during the training phase. In this paper, the particle swarm optimization (PSO) method is used to train an ANN to solve the EIT problem. It has been found that, compared with the back-propagation algorithm, PSO is capable of generating both faster and higher convergence. This paper also shows that the proposed method is capable of dealing with noisy data and the imperfections in the finite-element discretization, an important source of errors in EIT imaging.