Abstract: The processing of spatial variable is an important part of solving particle transport equation in discrete ordinates method, and it is more sensitive to the shielding calculation. It is so easy to bring negative flux for the traditional diamond difference scheme that many codes use a zero negative fixup algorithm. Although the algorithm eliminates the negative flux, however, the accuracy of diamond difference scheme is lost. Meanwhile, it causes flux distortions in space. The non-negativity of the extrapolated flux can be assured in weighted diamond difference scheme and theta weighted difference scheme. Based on the theta weighted difference scheme, the directional theta weighted difference scheme adopted directional theta weight to mitigate the distortions in some way. In the NATELSON benchmark, compared with DORT the maximum relative deviation of flux is 2.7%. The results of several shielding benchmarks demonstrate that the directional theta weighted difference scheme is more adaptable in the deep penetration problems.