In this talk, I will present a new p-multigrid method for solving the p-version symmetric interior penalty discontinuous Galerkin (SIPDG) discretization of elliptic problems. Using the polynomial iterations, we provide a rigorous convergence analysis for the proposed W-cycle p-multigrid method with respect to both the mesh size h and the degree of polynomials p, provided that the number of smoothing steps is comparable to p on each level. Moreover, we proved that our p-multigrid method is also robust with discontinuous diffusion coefficients.