This paper proposes a new method for the inverse problem of the three-dimensional reconstruction of the electrical activity of the brain from electroencephalography (EEG). Compared to conventional direct methods using additional parameters, the proposed approach solves the EEG inverse problem iteratively without any parameter. We describe the Lagrangian corresponding to the minimization problem and suggest the numerical inverse algorithm. The restriction of influence space and the lead field matrix reduce the computational cost in this approach. The reconstructed divergence of primary current converges to a reasonable distribution for three dimensional sphere head model.