We address the problem of direction-of-arrival (DOA) estimation for compressive sensing based multiple-input multiple-output (CS-MIMO) radar. The spatial sparsity of the targets enables CS to be desirable for DOA estimation. By discretizing the possible target angles, a overcomplete dictionary is constructed for DOA estimation. A structural sparsity Bayesian learning framework is presented for support recovery. To improve the recovery accuracy and speed up the Bayesian iteration, a subspace sparse Bayesian learning algorithm is developed. The proposed scheme, which needs less iteration steps, can provides high precision DOA estimation performance for CS-MIMO radar, even at the condition of low signal-to-noise ratio and coherent sources. Simulation results verify the usefulness of our scheme.