A new quasi-2D-Newton scheme is proposed for the steady-state 2-D numerical simulation of MOSFETs, in which a new quasi 2-D method is used to predict a good initial guess for the full Newton method. It is shown that the CPU time using our quasi-2-D-Newton scheme is shorter than that using the conventional Gummel-Newton scheme by a factor of two under the same specified stopping criterion. Furthermore, the maximum iteration-steps of the linear solution method (the SLOR method) must be reduced in order to improve the CPU-time performance of the simulation. Two procedures used to limit the iteration-steps of the SLOR method have been analyzed. Based on the analysis, five SLOR-iterations are taken and the CPU time can be reduced by at least a factor of three.