An analytic method is presented to estimate the evolution of electrical charge distribution inside the human brain related to the evoked potentials observed on the head surface. A three-layered concentric spherical human head model is adopted to express the relation between the observed potentials on the head surface and the spatial charge distribution inside the brain. In this context an integral equation associated with the three-layered concentric head model Green’s function is employed. Assuming the electric potentials are measured on the head surface, the charge distributions inside the human brain are computed by solving an inverse problem. To this end the Green’s function integral equation is inverted by using an algebraic reconstruction technique widely employed in X-ray tomography imaging. The accuracy of the proposed technique is examined by employing computer simulations and by checking the self-consistency of the developed algorithm.