In the circumstances that some sources are of finite distance to an array system, most high-resolution bearing estimation techniques exhibit unsatisfactory performance due to the invalidity of the planar wavefront assumption. This problem has been tackled by a far-field approximation (FFA) method based on a preprocessing scheme. By exploiting favorable characteristics of a uniform linear array, the FFA method constructs a FFA covariance matrix, which is Toeplitz and approximates to the far-field data covariance matrix, from the observed data covariance matrix. Then eigenstructure methods can be applied based on the FFA covariance matrix to perform bearing estimation without revising the planar wavefront assumption. In this paper, we extend this method for the problem of two-dimensional (2-D) angle-of-arrival (AOA) estimation using a uniform planar array in the presence of finite distance sources. A new procedure is derived for reconstructing the 2-D FFA covariance matrix with block-Toeplitz structure. Based on the 2-D FFA covariance matrix, we can apply eigenstructure methods in conjunction with a 2-D AOA search to solve the problem. Simulation results confirm the theoretical work.