This study describes the generalized multigroup energy treatment for the neutron transport equation. Discrete Legendre orthogonal polynomials (DLOPs) are used to expand the energy dependence of the angular flux into a set of flux moments. The leading (zeroth)-order equation is identical to a standard multigroup solution, while the higher-order equations are decoupled from each other and only depend on the leading-order solution because of the orthogonality property of the DLOPs. This decoupling leads to computational times comparable to the coarse-group calculation but provides an accurate fine-group energy spectrum. One-dimensional single-assembly and core calculations were performed to demonstrate the potential of the discrete generalized multigroup method. Computational results show that the discrete generalized multigroup method can produce an accurate fine-group whole-core solution for less computational time. A source update process is also introduced that provides improvement of integral quantities such as eigenvalue and reaction rates over the coarse-group solution.