Neutronics calculations are the basis of reactor analysis and design. Due to the rigorous mathematical and the flexibility of handling complex geometric domains and boundary conditions, finite element methods have gained more and more attention in solving neutron transport problems. In order to reduce the computational errors caused by the homogenization of cross sections, this paper adopts discontinuous Galerkin finite element 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 is generally more accurate than the classical continuous Galerkin finite element method if the same mesh is used. In additions, parallel computation ensures efficient solution of large-scale problems by the method.