In this paper，the theory and method are described in detail for solving two-dimensional neutron transport equation in cartesian geometry by using Flat Leakage Discrete Nodal Transport Method (FLDNTM). Based on this，a Linear Leakage Discrete Nodal Transport Method (LLDNTM)，more accurate than FLDNTM，is developed. Two computer codes-FLDNTM & LLDNTM，are created and applied to the calculations of one-and two-dimensional test problems，the excellent numerical results are obtained