Aiming at the nonuniform weighting for covariance lags in virtual array interpolation, the covariance matrix reconstruction of the coprime array is modeled as the low-rank matrix completion and atomic norm reconstruction. A novel covariance matrix reconstruction algorithm based on atomic norm for coprime array is proposed. Firstly, the Generalized Augmentation Approach(GAA) is utilized to obtain a partial covariance matrix of the coprime array. Then the partial covariance matrix is completed with the truncated mean singular value threshold method and reconstructed through the atomic norm minimization. A robust positive definite Toeplitz covariance matrix is accomplished. The proposed algorithm makes full use of the information contained in the coprime array to improve the stability of Direction of Arrival(DOA) estimation algorithm and reduce the computational complexity.