We present a local adaptive diffusion synthetic acceleration (DSA) method for neutron transport calculations. This new DSA method, called DG-DSA, solves the diffusion equation on a coarse mesh using the interior penalty discontinuous Galerkin (DG) methods. We investigate various numerical aspects of the DG-DSA method such as convergence performance and local adaptation. We demonstrate that our DG-DSA method can effectively and efficiently accelerate transport source iterations.