Abstract: With the first order neutron multi-group transport equation discretized using the discrete ordinates solution (S_N), a calculation model was established by using finite element method (FEM) based on single element and sweep method based on unstructured meshes. In a preset triangular element, the flux was discretized using Galerkin variation, and a linear system of equations was obtained. The angular flux of the nodes in the triangle element can be got by solving the linear system of equations, with offering some conditions. With the sweep method, all triangular elements will be swept and the differential equation can be solved. Based on the above theoretical model, the program FEGT was encoded. In order to validate this program, a series of examples were calculated. The results show that FEGT code meets the precision requirement.