We study the enhancement of accuracy, by means of the convolution post-processing technique, for discontinuous Galerkin(DG) approximations to hyperbolic problems. Previous investigations have focused on the superconvergence obtained by this technique for elliptic, time-dependent hyperbolic and convection-diffusion problems. In this paper, we demonstrate that it is possible to extend this post-processing technique to the hyperbolic problems written as the Friedrichs’ systems by using an upwind-like DG method. We prove that the L
2-error of the DG solution is of order k+1/2, and further the post-processed DG solution is of order 2k+1 if Qk
-polynomials are used. The key element of our analysis is to derive the (2k+1)-order negative norm error estimate. Numerical experiments are provided to illustrate the theoretical analysis.