Abstract: An analytic basis function expansion nodal method for directly solving the two-group neutron diffusion equation in the triangular geometry without transverse integration was proposed.The distributions of homogeneous neutron flux within a node were expanded into a set of analytic basis functions satisfying the diffusion equation at any point in a triangular node for each group.To improve the nodal coupling relations and computational accuracy,nodes were coupled with each other with both the zero-and first-order partial neutron current moments across all the three interface of the triangle at the same time.To simplify the derivation,coordinate conversion was used to transform the arbitrary triangle to regular triangle.With a new sweeping scheme developed for triangular geometry,the response matrix technique was used to solve the nodal diffusion equations iteratively.Based on the proposed model,the code ABFEM-3T was developed.Both rectangular and hexagonal assembly benchmark problems were calculated to validate the accuracy of the program.The numerical results for the series of benchmark problems show that both the core multiplication factor and nodal power distribution are predicted accurately.So this method can be used in complex unstructured neutron diffusion problems.