To solve the problem that Direction of Arrival(DOA) estimation based on virtual array interpolation does not fully utilize covariance matrix information, the reconstruction of covariance matrix of coprime array is transformed into low-rank matrix completion and atomic norm optimization, and proposes the reconstruction algorithm of covariance matrix of mutual array based on atomic norm.In this algorithm, the Toeplitz covariance matrix is expressed as the Toeplitz completion problem by the generalized augmented method, and then the truncated singular value threshold(SVT) method is used as the reference in the atomic norm optimization problem to carry out the optimization solution and transformed to achieve fast positive definite Toeplitz covariance matrix reconstruction. The algorithm makes full use of the information contained in the coprime array to improve the stability of DOA estimation algorithm and reduce the computational complexity.