The sparse recovery algorithm needs to perform grid quantization processing in the angle space when DOA estimation is performed. Aiming at the problem that the quantization error introduced by the quantization process affects the estimation performance, this paper introduced the quantization error into the second-order moment model of the array output through the first-order Taylor expansion of the steering vector. Based on this model, an OMP algorithm that used noise subspace vectors to modify was designed to jointly estimate DOA and quantization error. The new algorithm based on the array covariance matrix was slightly sensitive to the dependency on the number of snapshots, but it made up for the lack of DOA resolution of the greedy algorithm and did not require the number of sources to be predicted. At the same time, the amount of calculation was compared with the existing convex based on the Lp norm constraint. The optimization method was greatly reduced. Simulation experiments verify the effectiveness of the proposed algorithm.