The nonlinear Poisson problems are very common in heatconduction and diffusion with simultaneous reaction in a porous catalystparticle, so the generalized quasilinearization theory is exploited and anew numerical iterative method is proposed for this type nonlinear Poissonproblem. In this method, the nonlinear equation is replaced by a set ofiterative linear equation. An advantage of this method is that a theorybackground is substantial for the choice of the initial value of theiteration, and with a wide range of initial value the result of thisiteration is monotonously converged to the exact value. This new iterativemethod is combined with boundary element method and dual reciprocity hybridboundary node method for solving nonlinear Poisson problems, and theaccuracy, the convergence rate and stability with different initial valuesof these two methods are compared with each other. It is shown that, themethod based on dual reciprocity hybrid boundary node method and generalizedquasilinearization theory, has the high stability and efficiency, and theiterative rate is quadratic.