Neutronics calculations are the basis of reactor analysis and design. Finite element methods (FEM) have gained increasing attention in solving neutron transport problems for the rigorous mathematical formulation and the flexibility of handling complex geometric domains and boundary conditions. In order to reduce the computational errors caused by the homogenization of cross sections, this paper adopts the discontinuous Galerkin finite element method (DG-FEM) to solve the generalized eigenvalue problem formulated by the neutron diffusion theory and compensates the homogenization error by incorporating discontinuity factors. The results show that the discontinuous Galerkin finite element method can introduce the discontinuity factors with clear mathematical and physical meanings. The computational results of the discontinuous Galerkin finite element method are slightly better than those of the continuous Galerkin finite element method. However, the computation cost of the former is higher than that of the latter. Although good parallel efficiency can be achieved, the discontinuous Galerkin finite element method is not preferable for large-scale problems unless the effect of the discontinuity factors is significant.