In this paper, we propose an Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) based algorithm for estimating the two-dimensional-direction-of-arrivals (2D-DOA) of signals impinging on a uniform rectangular array (URA). The basic idea of the proposed algorithm is to successively apply two rounds of one-dimensional ESPRIT (1D-ESPRIT) algorithm for 2D-DOA estimation. The first round 1D-ESPRIT is applied on columns of the URA whereas the other round 1D-ESPRIT is on the rows of the URA. In between, a grouping technique is developed to produces signal groups each containing signals with distinguishable spatial signatures. The grouping technique is performed by using the subspace projection method where the needed spatial information is provided by the first round 1D-ESPRIT algorithm. Computer simulations show that, in addition to having significantly reduced computational complexity, the proposed algorithm possesses better estimation accuracy as compared to the conventional 2D-ESPRIT algorithm.