Distributed array radars consist of multiple sub-arrays separated by tens to hundreds of wavelengths and can match narrow beamwidths with large-aperture, high-gain antennas. The physical independence of the sub-arrays contributes to significant structure flexibility and is one of the advantages of such radars. However, a typical problem is the grating lobes in the digital beam forming (DBF) beam pattern. Unfortunately, the need to suppress the generation of grating lobes makes the design of acceptable sub-array arrangements very difficult. A sigma-delta beam former direction of arrival (DOA) estimation method is proposed in this study to solve this problem. The proposed method performs DOA estimation by acquiring the difference signals in addition to the sum signals of all sub-arrays. The difference signal is typically used for monopulse DOA estimation in the phased array radar. The sigma-delta beamformer simultaneously has both advantages of DOA estimations using a distributed array with a large aperture length and using a sub-array that is not affected by the grating lobe. The proposed method can improve the DOA estimation accuracy over the conventional method under grating lobe situations and help the distributed array radar achieve flexibility in the sub-array arrangement. Numerical simulations are presented to verify the effectiveness of the proposed DOA estimation method.