In this paper, it is shown how 2-D continuous compressive sensing (CCS) is used to recovery the complete measurements of a uniform rectangular array from its sparse case. 2-D CCS is implemented by reweighted atomic norm minimization. Based on the recovered data covariance matrix, the 2-D directions of arrival (DOA) are estimated via the Vandermonde decomposition of Toeplitz-block-Toeplitz matrix. Further, we present an enhanced approach by enlarging the virtual aperture of a sparse rectangular array. This approach can estimate more targets than the conventional one. Some typical examples are used to show the performance of the proposed 2-D DOA estimation method.