A new iterative method for solving the discretized nonlinear Poisson equation of semiconductor device theory is presented. This method has two main advantages. First, it converges for any initial guess (global convergence). Secondly, the values of electric potential are updated at each mesh point by means of explicit formulas (that is, without the solution of simultaneous equations). The first property makes this method quite robust, while the second allows for the implementation of the method on computers with small RAMs. Some numerical results obtained by this method are reported.