This work deals with directional of arrival (DOA) estimation with a large antenna array. We first develop a novel signal model with a sparse system transfer matrix using an inverse discrete Fourier transform (DFT) operation, which leads to the formulation of a structured block sparse signal recovery problem with a sparse sensing matrix. This enables the development of a low complexity message passing based Bayesian algorithm with a factor graph representation. Simulation results demonstrate the superior performance of the proposed method.