Abstract: The existing sparse reconstruction algorithms for DOA estimation algorithms couldn’t suppress noise and be applied in the background of colored Gaussian noise. In order to solve these problems, an approach for DOA estimation based on sparse reconstruction of fourth-order cumulant matrix was proposed in this paper. Firstly, we constructed sparse representation model using fourth-order cumulants of received data. Noise is suppressed in the model. Secondly, singular value decomposition was used upon forth-order cumulant matrix to simplify the sparse representation model. Through singular value decomposition, we not only reduced the scale of data, but also further suppressed noise. Aiming at solving the model, we selected weight vector using orthogonality between signal subspace and noise subspace. Then we solved the model by weighted 1 norm algorithm to achieve DOA estimation. Theoretical analysis and experimental results show that the algorithm proposed in this paper can be applied in the background of white Gaussian noise and colored Gaussian noise. The algorithm has the capability of processing both incoherent and coherent signals and achieves more accurate estimation for coherent signal in the case of low SNR. Compared with the same kind of sparse reconstruction algorithms, the algorithm has lower calculation complexity and higher angle resolution.