Abstract: In this paper, a convergent two-dimensional numerical simulation method for transport characteristics of intense ion beams in acceleration-deceleration system is presented.Our problem requires the simultaneous solution of:(1) the nonlinear Poisson's equation, (2)tne non-relativistic equation of ion motion; (3)the con-tintity of ion current. Because of the complexity of the boundary geometries, finite element method is used to solve Eq.(1)And the computer program was developed. The self-consistent results of space potential distribution, ion trajectories and distribution of ion space charg density are given. The method is suitable to study transport problem of intense ion beams in acceleration -deceleration system, in particular, for high intensity ion implantation facility, intense ion beamsexten-sion, intense plasma ion source and so on.