This paper addresses the direction of arrival (DOA) estimation problem for the co-located multiple-input multiple-output (MIMO) radar with random arrays. The spatially distributed sparsity of the targets in the background makes com-pressive sensing (CS) desirable for DOA estimation. A spatial CS framework is presented, which links the DOA estimation problem to support recovery from a known over-complete dictionary. A modified statistical model is developed to ac-curately represent the intra-block correlation of the received signal. A structural sparsity Bayesian leaing algorithm is proposed for the sparse recovery problem. The proposed algorithm, which exploits intra-signal correlation, is capable being applied to limited data support and low signal-to-noise ratio (SNR) scene. Furthermore, the proposed algorithm has less computation load compared to the classical Bayesian algorithm. Simulation results show that the proposed algorithm has a more accurate DOA estimation than the traditional multiple signal classification (MUSIC) algorithm and other CS recovery algorithms.