The recently developed linear prolongation Coarse Mesh Finite Difference (lpCMFD) acceleration scheme, which employs a linear additive approach to update the scalar flux, has been shown to be more stable and effective than the conventional scaling-based Coarse Mesh Finite Difference (CMFD) method for accelerating the discrete ordinates (SN) neutron transport calculation using spatial finite difference discretization. In this paper, we study and extend the application of lpCMFD to accelerate the SN neutron transport calculation with spatial discretization using the Discontinuous Galerkin Finite Element Method (DGFEM), which generally involves linear- or higher-order space expansion functions. A function space mapping operator is proposed in this paper to project the lpCMFD linear-order correction flux to an arbitrary-order DGFEM basis function, which is implemented and tested on a one-dimensional (1-D) in-house–developed DGFEM-based SN code. The consistency between the lpCMFD accelerated results and the pure SN results is naturally guaranteed by employing upwind current information from DGFEM-based SN transport calculation to evaluate the drift coefficient. It was found from our numerical testing with the CMFD and the lpCMFD acceleration schemes on single-group fixed-source and k-eigenvalue problems that both acceleration schemes can reproduce the unaccelerated scalar flux and keff, respectively. Further numerical testing on a more realistic case is performed on a 1-D slice multi-energy-group problem based on the three-dimensional C5G7 mixed oxide (MOX) benchmark. It was found that by using the function space projector proposed in this paper, lpCMFD was stable and effective to accelerate the DGFEM-based SN neutron transport calculation for all coarse mesh sizes tested while CMFD diverged for large optical thickness.