Different from traditional direction of arrival (DOA) estimation algorithms such as steered response power phase transform (SRP-PHAT) algorithm and delay-and-sum (DS) algorithm, the compressed sensing (CS) microphone arrays DOA algorithm transforms the sound source localization into the reconstruction problem of sparse signal to achieve better performance. However, in practical application environment, the direction vector of the far-field sound source tends to exhibit block sparseness due to the sound source directivity, the spatial reverberation and other reasons, which leads to the performance degradation of traditional sparse recovery algorithms such as orthogonal matching pursuit (OMP) algorithm. In this paper, the block approximated l₀ is introduced into the microphone array CS DOA algorithm. Under the CS framework, the block approximated l₀ sparse recovery is used to reconstruct the direction vector of the sound source to obtain DOA. Experimental results show that the proposed algorithm is capable of yielding higher positioning accuracy compared with traditional algorithms and traditional sparse recovery algorithm using OMP algorithm.