A general acceleration scheme for the iterative transport calculations is analyzed, and the implementation of this scheme in the two-dimensional transport code TWOTRAN PNWV is described. The convergence radius is estimated for homogenous one-dimensional slab problems. Two-dimensional benchmark problems are used to outline the dependence of the convergence on the material properties and on the fine- and coarse-mesh grids. Possible applications of this scheme to obtain acceleration methods for other iterative algorithms are suggested.