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It is well know that the performance of the minimum variance distortionless response (MVDR) beamformer is very sensitive to steering vector mismatch because of the signal cancellation. Such mismatches can occur as a result of direction-of arrival (DOA) errors, local scattering, near-far spatial signature mismatch, waveform distortion, source spreading, imperfectly calibrated arrays and distorted antenna shape. In this paper, an adaptive beamformer which is robust against the DOA mismatch is proposed. This method imposes two quadratic constraints such that the magnitude responses of two steering vectors exceed unity. Then a diagonal loading method is used to force the magnitude responses within a range of the arrival angles to exceed unity. The diagonal loading factor can be computed systematically by a proposed algorithm. Numerical examples show that this method has a significantly better SINR performance compared to previously published methods (including the MVDR), and a complexity comparable to the standard MVDR beamformer.