In this paper,we propose improved approaches for two-dimensional (2D) direction-of-arrival (DOA) estimation for a uniform rectangular array (URA).Unlike the conventional eigenstructure-based estimation approaches such as Multiple Signals Classification (MUSIC) and Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT),the proposed approaches estimate signal and noise subspaces with Nystr(o)m approximation,which only need to calculate two sub-matrices of the whole sample covariance matrix and avoid the need to directly calculate the eigenvalue decomposition (EVD) of the sample covariance matrix.Hence,the proposed approaches can improve the computational efficiency greatly for large-scale URAs.Numerical results verify the reliability and efficiency of the proposed approaches.