Abstract: Using the theory of area coordinate,arbitrary triangles were transformed into regular triangles.The transverse integration was done on the regular triangle.The spatial distribution of intra-node flux and source were approximated by a new orthogonal quadratic polynomial expansion,and a second-order polyno-mial provided the spatial expansion of transverse-leakage.The neutron angular distribution of flux and trans-verse-leakage were represented by the S_N quadrature set.Additionally,the nodal-equivalent finite difference algorithm was applied in order to establish a stable and efficient iterative scheme.A two-dimension triangular nodal S_N transport calculation program（DNTR） was coded according to the model.A series of numerical results for the test problems demonstrate that this triangular nodal S_N method is faster 5 to 7 times than the fine mesh difference code（DOT4.2） with the same precision and faster 1 to 3 times than the rectangular dis-crete nodal transport method（DNTM） with the same precision and equal mesh width.However,this method can be applied to solve the unstructured neutron transport problems,and has an unexampled advantage of the nodal S_N methods used on the structured meshes,such as DNTM.