When the conventional Space-Alternating Generalized Expectation-maximization (SAGE) algorithm is used to estimate the incident angle of the signal received by an antenna array with fixed aperture, the accuracy and resolvability of angle estimation are affected and limited by the aperture of the antenna array. Therefore, in order to improve the angle estimation accuracy and resolvability beyond the limitation, we propose a beamforming (BF)-incorporated SAGE (BFI-SAGE) algorithm, which is a SAGE-based improved high-resolution parameter estimation (HRPE) algorithm, and it steers the orientation of beam utilizing a predefined BF weighting matrix. A non-uniform scanning mode is determined to achieve higher angle estimation accuracy in the angle range of interest, and the analysis of the angle estimation performance is performed for the cases of uniform and non-uniform scanning modes, respectively. The resolvability performance of the algorithm is also discussed.