We present some two-level nonoverlapping and overlapping additive Schwarz methods for a discontinuous Galerkin method for solving second order elliptic problems. It is shown that the condition numbers of the preconditioned systems are of the order for the nonoverlapping Schwarz methods and of the order for the overlapping Schwarz methods, where h and H stand for the fine-mesh size and the coarse-mesh size, respectively, and denotes the size of the overlaps between subdomains. Numerical experiments are provided to gauge the efficiency of the methods and to validate the theory.