As is well known, nonuniform linear arrays have significant advantages in array aperture and degrees of freedom over uniform linear arrays. Using their difference coarrays, subspace-based approaches can be utilized to perform underdetermined and high-resolution direction-of-arrival (DOA) estimation. However, the subspace-based approaches depend on the covariance matrix reconstruction in the coarray domain, which are not statistically efficient when the number of sources is more than one and less than the number of sensors. In this paper, to overcome this drawback, we devise an augmented covariance matrix reconstruction algorithm for DOA estimation in the coarray domain. The proposed algorithm recovers the complete augmented covariance matrix by solving a rank-minimization problem. But unlike the conventional schemes, it exploits the estimation error distribution of the incomplete augmented covariance matrix to derive the constraint condition of the rank-minimization problem. Based on the reconstructed augmented covariance matrix, we can enhance the DOA estimation performance for multiple source scenario at high signal-to-noise ratio. Although our algorithm is developed based on the non-consecutive coarray, it is also suitable for the consecutive coarray. Numerical results demonstrate the superiority of the proposed algorithm over several existing approaches.