We propose a very simple but efficient postprocessing technique for improving the global accuracy of the discontinuous Galerkin (DG) time stepping method for solving nonlinear Volterra integro-differential equations. The key idea of the postprocessing technique is to add a higher order generalized Jacobi polynomial of degree k+1 with parameters (−1,0) to the DG approximation of degree k. We prove that the postprocessed DG approximations converge one order faster than the unprocessed DG approximations in the L2-, H1- and L∞-norms. Based on these postprocessed superconvergence results, we construct several a posteriori error estimators and prove that they are asymptotically exact as the step-size decreases. Numerical experiments are carried out to verify the theoretical results.